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Samantha says that a 180 degree rotation, with center P, has the same effect on points in the plane as reflecting over line m. True or False?

Samantha says that a 180 degree rotation, with center P, has the same effect on points in the plane as reflecting over line m. True or False?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Lines l and m are perpendicular with point of intersection P.

m ⊥ l

Samantha says that a 180 degree rotation, with center P, has the same effect on points in the plane as reflecting over line m. True or False?

The image depicts a Cartesian coordinate system with two lines, labeled \( m \) and \( l \), intersecting perpendicularly at a point labeled \( P \). - Line \( m \) is vertical, extending upwards and downwards from the point \( P \). - Line \( l \) is horizontal, extending to the left and right from the point \( P \). - At their intersection, there is a right angle, indicated by a small square at \( P \), demonstrating that the lines are perpendicular to each other. This diagram is a basic representation of orthogonal lines in geometry, demonstrating the concept of perpendicularity within a plane.
Transcribed Image Text:The image depicts a Cartesian coordinate system with two lines, labeled \( m \) and \( l \), intersecting perpendicularly at a point labeled \( P \). - Line \( m \) is vertical, extending upwards and downwards from the point \( P \). - Line \( l \) is horizontal, extending to the left and right from the point \( P \). - At their intersection, there is a right angle, indicated by a small square at \( P \), demonstrating that the lines are perpendicular to each other. This diagram is a basic representation of orthogonal lines in geometry, demonstrating the concept of perpendicularity within a plane.
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