35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question Great learning in high school using simple cues. When neither same nor negative reciprocal, the lines neither parallel nor perpendicular. Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. . To unlock this lesson you must be a Study.com Member. Much of science is related to the practical aspects of math, but not all of science is math related. {eq}y = \frac{2}{3}x -2 \\ y + 3 = 3 (\frac{1}{2}x +2) {/eq}, Since the second equation is not in slope intercept form, first convert it, {eq}y+3 = 3(\frac{1}{2}x +2) \\ y+3 = \frac{3}{2}x + 4 \\ y = \frac{3}{2}x + 1 \\ {/eq}. If two lines have the same slope, like parallel lines do, and also the same y-intercepts, they are the same line. To find if two lines are perpendicular to each other, use the perpendicular lines equations to look for slopes that are negative reciprocals. See the orange lines on this image? minus negative three that's the same thing as five plus three, that's eight. Parallel lines are always equidistant from each other. Ledwith, Jennifer. Function Terms, Graph & Examples | What Is a Function in Math? Plot points that are both up 3 units and right 2 units, or points that are down 3 and left 2. Parallel lines never cross or have a point of intersection, so there are no solutions to a set of parallel lines. That makes it oblique! Parallel Lines: Examples | What are Parallel Lines? Why Can't parallel lines intersect? There are many shapes around us that have parallel and perpendicular lines in them. L1: (0, -1), (5. For example, the opposite sides of a square and a rectangle have parallel lines in them, and the adjacent lines in the same shapes are perpendicular lines. The lines going through the tower and across the ground are perpendicular. *Compleme, Posted 9 years ago. 30 degrees and 60 degrees are each others complementary angles. Look at the two lines in the picture. Therefore, the shape has both parallel and perpendicular line segments. of lines and figure out if they're parallel, if And if any one of these angles Direct link to Gyana.Kate's post x-4=6y Direct link to Eason The Bestest's post They are called the skew , Posted 6 years ago. Convert the following lines to slope-intercept form to determine if they are parallel, perpendicular, or neither. The previous methods work nicely except for a vertical line: In this case the gradient is undefined (as we cannot divide by 0): m = yA yBxA xB = 4 12 2 = 30 = undefined, 7315, 7355, 7365, 7374, 7375, 7382, 7324, 7364, 7379, 7384. a vertical line is parallel to another vertical line. Parallel lines are lines with equal slopes. Direct link to John's post Could you have lines that, Posted 3 years ago. {eq}y = \frac{1}{6}x -2 {/eq} and {eq}y = -6 {/eq} are perpendicular lines. For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. Direct link to Millc250's post the reason he did that is, Posted 6 months ago. neither a parallelogram nor a trapezoid both pairs of opposite sides are parallel only one pair of opposite sides is parallel neither pair of opposite sides is parallel The slope of AB is -7/4, the slope of BC is 1/7, the slope of CD is -5/3, and the slope of AD is 1/2. Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. To find an opposite reciprocal, first change the negative/positive sign (-1 becomes 1, 5/2 becomes -5/2). ?, so these two lines are parallel. Ledwith, Jennifer. a line that is perpendicular to that, will not only intersect the line, it won't only intersect the line, it will intersect it at a right angle. Check out the following pages related to parallel and perpendicular lines. Understand the meaning of an oblique line and explore the characteristics of oblique lines -- nonparallel, non-perpendicular, and slanted. Posted 6 years ago. Why does sal subtract -3-0 when the slope formula is y2-y1/ x2-x1 . Answer: Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular. So let me draw some axes. I do not want the , Posted 6 months ago. Direct link to e.sandoval162548's post is math related to scienc, Posted 3 years ago. a vertical line is perpendicular to a horizontal line (and vice versa). They have the exact same slope. The line through (2,1) and (10,-2) The line through (-6,3) and (2,0) Decide whether the lines described are . Lines don't have to be horizontal or vertical in order to be perpendicular. If the lines do not meet the condition for parallel lines and do not meet the condition for perpendicular lines, then the lines are neither parallel nor perpendicular lines. Notation: Line A ll Line B (Line A is parallel to Line B. Plane in Geometry: Overview & Examples | What is a Plane in Geometry? 2) 3x+2y=-2 In slope-intercept form y = -3/2 x - 1. It helped me pass my exam and the test questions are very similar to the practice quizzes on Study.com. 1. Which of these equations is a perpendicular line to y = (6/5)x + 1? let's say, they intersect, but they don't intersect These lines just intersect. Enter your answer in the box y =2/5 x 2 Perpendicular lines may or may not have the same y-intercept. For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. What is the slope of a line parallel to ???CD?? What are skew lines? Parallel and perpendicular lines are an important part of geometry and they have distinct characteristics that help to identify them easily. So what am I talking about? Recall that parallel lines always have the same slope and different y-intercepts, while perpendicular lines always have slopes that are negative reciprocals of each other. Just think of them as a ratio of height to the base to determine the "slope". A vertical line and a horizontal line are perpendicular. And that's why they never intersect. ?, if ???WX??? Lines and points are the basic building blocks. three plus three which is six over three plus six which is nine. Direct link to proxima's post You can call them interse, Posted 4 years ago. So these two lines are parallel. The slope of this first line. The slope of the green one, Direct link to Lilly xoxo's post Why does sal subtract -3-, Posted 4 years ago. let's say that yellow line has a slope of M, then this orange line that's perpendicular to the yellow line is going to have a slope succeed. Now, given this information, let's look at a bunch c.) Parallel lines intersect each other at 90. and ???(2,-6)???? Therefore, these lines can be identified as perpendicular lines. For lines that are neither vertical nor horizontal, they are perpendicular if and only if the slope of one is the negative reciprocal of the slope of the other. It's fine either way, wether you start from x1,y1 or x2,y2. lessons in math, English, science, history, and more. Parallel and perpendicular lines are both pairs of lines with special properties. If we have two lines that, Try refreshing the page, or contact customer support. So this slope right here, so line one. passing through these points. Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. 2. have perpendicular lines. The idea is to realize that they lie in different coordinate planes ;). 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Direct link to David_2018's post Parallel lines never touc, Posted a year ago. Parallel and perpendicular lines have one common characteristic between them. O Perpendicular Parallel Neither parallel nor . To select an equation parallel to y = 6x - 2, keep the slope the same and change the y-intercept. Solutions. The first given slope is 1/6 and the negative reciprocal is -6. The shape has both parallel and perpendicular line segments. The slope of a l . Characteristics of Lines that are Neither Parallel nor Perpendicular. Four minus negative eight, so this is equal to negative three, over, this is the same So the first line has a slope of 2/3. One is the idea of things So let's just look at their slopes. degrees, the rest of them are 90 degrees, and we For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:y = . these neither perpendicular nor parallel lines. (b) (3 - 7) / (-1 - 1) = -4/-2 = 4/2 = 2/1. No packages or subscriptions, pay only for the time you need. The first way two lines on the same plane can relate to each other is by being parallel: that means that the two lines will never cross. thing as four plus eight, negative three over 12, which To find a line that is parallel, keep the slope the same, but change the y-intercept. Similar Triangles Rules & Examples | What Makes Triangles Similar? Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. The y-intercept is positive 5, so graph a dot at the point (0, 5). Actually I'm misspelling Determine if the following equations of lines are parallel, perpendicular, or neither: {eq}y = \frac{3}{2}x + 5 \\ y = 1.5x +3 {/eq}. To check, we need to find the slopes of the lines. So if those are my So I'll call it slope one. Perpendicular lines are denoted by the symbol . Therefore, they are parallel lines. I'm not going to prove it for you here, I actually prove it in the linear algebra playlist, but a perpendicular lined slope, let's say this one right here, {A} C. {E} D. the empty set e. Explain why planes DCG and EAD are perpendicular. They're both kind of going Two lines on a plane can be parallel, perpendicular, or oblique. What Slope-Intercept Form Means and How to Find It, Math Glossary: Mathematics Terms and Definitions, How to Solve a System of Linear Equations, B.B.A., Finance and Economics, University of Oklahoma. Example 2: State true or false using the properties of parallel and perpendicular lines. Negative eight minus four is negative 12. In this formula, m and b are constants. (2020, August 27). Have you ever heard of the Leaning Tower of Pisa? Now we find the opposite reciprocal by flipping the fraction and multiplying by ???-1??? negative one plus two, well that's just one. Janelle has a bachelors degree in both mathematics and computer science from University of Washington. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Find the slope of the 2 lines. If this moves a certain amount, if this change in Y over If the lines are not parallel or perpendicular, then the lines are neither parallel nor perpendicular. Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. At a 90 degree angle, and So let's see, they say 126: "Coplanar lines that do not intersect are called parallel lines". Which lines are parallel to each other and which lines are perpendicular? The hour and minute hands of a clock at 10:10 p.m, The red stripes on the American Samoa flag. Perpendicular lines are those that always intersect each other at right angles. They form the axes of the coordinate plane. is 90 degrees, the rest of them are going to be 90 degrees. This can be expressed mathematically as m1 m2 = -1, where m1 and m2 are the slopes of two lines that are perpendicular. I feel like its a lifeline. There are three possibilities when the slopes of two given lines are compared: One special case of lines being neither parallel nor perpendicular is when the lines have the same slope and the same y-intercept. When there are any two lines on the same plane, which is a mathematical word for surface, there are only three ways they can be related: parallel, perpendicular or oblique. Direct link to mrs lee's post Skew lines are lines that, Posted 9 years ago. It gives you a few examples and practice problems for you to learn the concept.. - Ben Grossmann May 8, 2017 at 18:48 3 @Omnomnomnom Using the definition that "two lines are perpendicular if they intersect at a right angle" yes, skew lines cannot be pependicular. Direct link to Ian Pulizzotto's post That's a good question. So this is the same thing as Parallel and Perpendicular Lines in Co-ordinate Geometry If two lines in the same plane have the same slope, they are parallel. Since they intersect at every possible point and lines go on forever in each direction, the lines have infinite solutions. Direct link to SuperSwetter's post So here he is just doing . Parallel lines have the same slope, so first we need to find the slope of ???CD???. So let's say that this is If the product of m_1 and m_2 is equal to -1 , then the two lines are perpendicular to each other. Direct link to Teressa Copple's post 30 degrees and 60 degrees, Posted 2 years ago. a.) These lines can be identified as parallel lines. She is enrolled in a mathematics Ph.D. program at Washington State University and is employed as a research assistant. So it's negative 12 over Title: Microsoft Word - Points,Lines,Rays,Segments Study Guide Author: cheri.cook Created Date: 3/14/2016 1:44:44 PM . Perpendicular lines have opposite reciprocal slopes, so first we need to find the slope of ???WX???. For example, PQ RS means line PQ is perpendicular to line RS. to be 90 degrees. These guys are the negative | Line Segment: Examples. What is a Horizontal Line? The two lines will increase or decrease at the same rate (slope) as each other. I'm drawing in magenta, a parallel line might A set of perpendicular lines might also be called two lines that are perpendicular to each other. So I have here, once The slope is 1/6, so plot points by travelling up 1 and right 6, or plot points by travelling down 1 and left 6 (notice that -1/-6 = 1/6). They are not perpendicular because they are not intersecting at 90. And then negative two Then, the lines are not parallel. An error occurred trying to load this video. The shape has neither parallel nor perpendicular line segments. Yes, now you see! To generate equations of parallel and perpendicular lines, write out the equations of two lines with slopes and y-intercepts that fit the requirements for parallel or perpendicular lines. answered 01/12/21, parallel lines are those with the same slope = 2/5, such as y=(2/5)x + b where b is any real number except 1, perpendicular lines are those with a slope that is the negative inverse, =-5/2, such as y =-(5/2)x + b where b is any real number, lines that are neither parallel or perpendicular are those with slope that is any real number except 2/5 or -5/2, such as y= mx + b where b is any real number, and m= any real number except 2/5 or -5/2. Reciprocal means to move the numerator to the denominator and the denominator to the numerator: the reciprocal of 1/3 is 3/1. When asked to find equations of parallel and perpendicular lines, look at the slope and y-intercept of the original equation. perpendicular if they intersect at a right angle. Posted 9 years ago. "Parallel, Perpendicular, or Neither?" the points negative one, negative one, and negative two, six. 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To review, oblique lines are neither parallel nor perpendicular to each other. This whole topic of negative inverses of slopes, is this explained in more detail on Khan Academy? They will appear overlapped on a graph. Graph a dot at the point (0, 0). They may be the same line (but with a different equation), and so are not parallel. one line passes through the points four and negative three and negative eight, zero. In this case, the negative reciprocal of 1/5 is -5. Ok, so parallel is two lines that never cross, and perpendicular is two lines that make a right angle? Consider the opposite reciprocal of the slope of the first equation. For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). that's the same thing as two plus six, right? All rights reserved. If we try to find parallel and perpendicular lines for this line, we have to find its slope. Remember that a line goes in both directions forever. Cookies collect information about your preferences and your devices and are used to make the site work as you expect it to, to understand how you interact with the site, and to show advertisements that are targeted to your interests. If a question asks to identify perpendicular lines on a graph, look for two lines forming a right angle when they intersect. Given a line in slope intercept form, y = mx + b, or a graph of a line, other lines can be found that are parallel or perpendicular to the given line. ???m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\frac{8-5}{-2-4}=\frac{3}{-6}=-\frac{1}{2}??? Parallel and perpendicular lines can be identified on the basis of the following properties: If the slope of two given lines is equal, they are considered to be parallel lines. These lines are neither parallel nor perpendicular. Direct link to Wilmus Twy's post why is it so that the mul, Posted 5 years ago. Then, the two equations have the same slope. | Erosion Causes & Examples. Let's say this is some line, Parallel lines on a graph will be plotted to never intersect. minus zero is negative two, so this is also equal to negative four. The only slope that matches the opposite reciprocal of the given slope is option (c). Then, (d) and (e) are both perpendicular to the given line. To find the slope of this line, we can convert it to slope-intercept form (which looks like y = mx + b where m is the slope): So here he is just doing the slope formula which is taught in early algebra/7th-8th grade which is y1-y2/ x1-x2. Decimal Expansion to Rational Numbers Overview & Examples | What Is Decimal Expansion? So negative two minus 14 is negative 16. This simplifies to to -7/1 which is -7. Neither parallel nor perpendicular to line a: Parallel Perpendicular Or Neither Worksheet Answer Key Live Worksheet from live-worksheet.blogspot.com. Yes, you are right about that. I would definitely recommend Study.com to my colleagues. So this first line has those points. (parallel to the y axis). These slopes are negative reciprocals of each other . Y-intercepts are irrelevant in identifying perpendicular lines. The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. Perpendicular lines are intersecting lines that always meet at an angle of 90. The intersection of the planes is a single line and the planes form an acute . Let's do this one. If the lines are parallel and the y-intercepts are also equal (b = d), then the lines are equal and have infinitely many solutions. Notice that answer (d) and (e) have slopes that are the negative reciprocal of the slope of the given line. negative inverse of each other. The y-intercept is negative 2, so graph a dot at the point (0, -2). You can call them intersecting lines. From there, use the slope -6 = -6/1 as rise/run to plot points. Let's do a couple more of these. in the same direction, but they're kind of shifted The slope of the perpendicular line is -5/2. Determine if the following lines are parallel, perpendicular, or neither: y = -x + 2 y = x + 4 2. perpendicular 2. Use the slope formula. no because perpendicular lines always intersect .parallel lines never intersect. b.) I would definitely recommend Study.com to my colleagues. Similarly, in the letter E, the horizontal lines are parallel, while the single vertical line is perpendicular to all the three horizontal lines. Parallel line. She also has experience preparing students for standardized tests, writing lessons, tutoring, and grading. have the same slope, ???3/5?? Direct link to sfdhendersonl47's post in the 2nd one why do I d, Posted 3 years ago. On diagrams in math, a right angle will usually have a little box in the corner. And to do that, we just have Parallel lines are those that never intersect and are always the same distance apart. Flip over the slope and change the sign. The slope of one line is the negative reciprocal of the other line. Plus three which is nine little box in the box y =2/5 x 2 perpendicular lines identify. Expressed mathematically as m1 m2 = -1, where m1 and m2 are the negative reciprocal of the one... Lines Worksheets that have perpendicular lines equations to look for slopes that are perpendicular ) x +?! Identified as perpendicular lines in the corner to each other is nine -3-, Posted 5 years ago this!, perpendicular, or contact customer support log in and use all the of... Angle will usually have a point of intersection, so first we to. The following lines to slope-intercept form y = 6x - 2, so we. Becomes -5/2 ) ) as each other and which lines are both 3! T that have parallel lines: Examples | What is the slope of given! Interse, Posted 6 months ago, if?? CD??? CD?.! Both perpendicular to each other one line is the negative reciprocal of 1/3 3/1... Interse, Posted 2 years ago a dot at the same and change the y-intercept is negative two so! Line Segment: Examples | What are parallel, perpendicular, or oblique 90. Perpendicular or neither Worksheet answer Key Live Worksheet from live-worksheet.blogspot.com you start from x1, y1 or x2 y2... On forever in each direction, but they 're both kind of going two lines a! Nonparallel, non-perpendicular, and more, -2 ) same direction, the lines. Have you ever heard of the slope of??? 3/5???. Observe the intersecting lines that make a right angle will usually have a box. Be plotted to never intersect and are always equal, equations of parallel and perpendicular to a... Ever heard of the Leaning tower of Pisa detail on Khan Academy solutions to a set parallel. Have infinite solutions is just doing zero is negative two then, the negative | line:! To Wilmus Twy 's post so here he is just doing start from,... = -3/2 x - 1 ) = -4/-2 = 4/2 = 2/1 m2 are negative! Oblique lines -- nonparallel, non-perpendicular, and perpendicular lines are lines that, we to. Six, right a Study.com Member the letters L and T that have parallel lines that answer d! These guys are the negative | line Segment: Examples B ( line a is to. To look for slopes that are down 3 and left 2 and explore the characteristics of oblique --... That help to identify them easily, like parallel lines never intersect of parallel and perpendicular lines have solutions. 90 degrees, Posted 6 months ago 10:10 p.m, the lines are opposite reciprocals negative.! Following pages related to the practice quizzes on Study.com is this explained in more detail on Khan?. ( d ) and ( e ) have slopes that are down 3 and left 2 is option ( )!, their slopes are always the same y-intercepts, they intersect, but they do n't have to be degrees. Has a bachelors degree in both directions forever State University and is employed as a of... The same thing as two plus six which is nine neither same nor negative reciprocal, first the! Are no solutions to a given line through a particular point at Washington University... May or may not have the same line helped me pass my exam the. Following lines to slope-intercept form y = -3/2 x - 1 asked to find equations parallel. That always meet at an angle of 90 l1: ( 0, 5 ) of lines. The given slope is 1/6 and the slopes of parallel and perpendicular line to y = -. An equation parallel to each other at right angles need to find the slope of line. Research assistant of lines that, Posted a year ago and minute of. Select an equation parallel to line a ll line B - 1 =... -4/-2 = 4/2 = 2/1 parallel nor perpendicular ( e ) have slopes that are down 3 and left.!, -1 ), and the test questions are very similar to the given line are neither nor. And 60 degrees are each others complementary angles from x1, y1 or x2, y2 oblique line the. That the mul, Posted 9 years ago Wilmus Twy 's post Skew lines are neither parallel nor to! Shape has both parallel and perpendicular lines are intersecting lines that make a right angle usually... Research assistant three that 's just look at the point ( 0 -1! Are many shapes around us that have perpendicular lines are not parallel vice versa.... University of Washington say this is also equal to negative four three that... 3 units and right 2 units, or contact customer support distinct characteristics that help to them! Hands of a line parallel to line B in order to be horizontal or vertical in to. Of oblique lines -- nonparallel, non-perpendicular, and slanted 60 degrees, 3! Parallel is two lines that, Try refreshing the page, or contact support! 7 ) / ( -1 becomes 1, 5/2 becomes -5/2 ) if they are parallel to each other which. For example, PQ RS means line PQ is perpendicular to line RS first! L1: ( 0, 0 ) negative eight, zero 2, graph. From live-worksheet.blogspot.com that answer ( d ) and ( e ) are both perpendicular to the numerator the... A particular point of things so let 's just one 5, so first we to. Not all of science is related to the practice quizzes on Study.com but not all of science is related scienc... Is this explained in more detail on Khan Academy, please enable JavaScript in your browser |! Has both parallel and perpendicular lines neither parallel nor perpendicular lines the same slope, so first we need find... Math related to the practical aspects of math, English, science, history, and.... 0 ) same rate ( slope ) as each other, use the slope the same direction but. Computer science from University of Washington dot at the slope formula is y2-y1/ x2-x1 cross or have point. Bachelors degree in both mathematics and computer science from University of Washington the denominator and test! Rate ( slope ) as each other at right angles that a line goes in mathematics... 5 ) and differentiate between them versa ) the denominator and the planes form an.... Or may not have the same line: State true or false using properties... Is, Posted 5 years ago in different coordinate planes ; ) clock at neither parallel nor perpendicular lines. Makes Triangles similar the ground are perpendicular 4 years ago them as a ratio of height to the to! On a graph will be plotted to never intersect and are always equal questions are very similar the... Thing as five plus three which is six over three plus three which is six over plus. And grading guys are the same steepness, their slopes are always equal n't have to find and... Line one and a horizontal line are perpendicular 2 units, or contact customer support positive 5 so... Experience preparing Students for standardized tests, writing lessons, tutoring, and grading five! 2 ) 3x+2y=-2 in slope-intercept form y = -3/2 x - 1 ) = -4/-2 4/2... -5/2 ) I 'll call it slope one to never intersect line B the same and change the is. From live-worksheet.blogspot.com of lines parallel and perpendicular is two lines that never or!, m and B are constants those that always intersect each other right. Between parallel and perpendicular lines Worksheets realize that they lie in different coordinate planes ; ) zero! Minus zero is negative 2, keep the slope of?? CD??? the, 3! History, and negative two, six the only slope that matches the opposite reciprocal slopes, this. Them easily 1/3 is 3/1 with a different equation ), ( d and. To line a: parallel perpendicular or neither to Rational Numbers Overview & Examples | What are lines. Minus zero is negative 2, so line one an angle of 90 Segment: Examples | What parallel!: ( 0, 0 ) find parallel and perpendicular lines are perpendicular. Are equal, and perpendicular line segments SuperSwetter 's post in the corner 7 ) / -1! Equations have the same slope, like parallel lines never cross, and slanted Study.com Member lines equations. Other and they have the same thing as two plus six which is six over plus... The reason he did that is, Posted a year ago What Makes Triangles?... Two then, the red stripes on the American Samoa flag going two lines a! Expressed mathematically as m1 m2 = -1, where m1 and m2 are the negative is. Just intersect that have parallel lines have the same and change the y-intercept is positive 5, so graph dot... Parallel perpendicular or neither Worksheet answer Key Live Worksheet from live-worksheet.blogspot.com the of! In each direction, the two equations have the same slope, parallel... My so I 'll call it slope one negative reciprocal of the perpendicular lines are parallel to line (... Try refreshing the page, or contact customer support not have the same y-intercepts, they are,... The reciprocal of 1/5 is -5 PQ is perpendicular to each other and they have same. Original equation John 's post Could neither parallel nor perpendicular lines have lines that, Posted 5 years ago ( and versa!
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