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(3) Recall that a map, f: R2 R2, is an isometry if |P - Q| = |ƒ(P) − f(Q)| for all pairs of points P and Q in R². Thus, f is a distance preserving map. Show that an isometry, f: R2 R2 also preserves angles. In other words if two line segments meeting at a point determine an angle a, their image line segments meeting at the image of that point also determine the angle a.

(3) Recall that a map, f: R2 R2, is an isometry if |P - Q| = |ƒ(P) − f(Q)| for all pairs of points P and Q in R². Thus, f is a distance preserving map. Show that an isometry, f: R2 R2 also preserves angles. In other words if two line segments meeting at a point determine an angle a, their image line segments meeting at the image of that point also determine the angle a.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 47PS
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(3) Recall that a map, f: R2 R2, is an isometry if |P - Q| = |ƒ(P) − f(Q)| for all pairs of points P and Q in R². Thus, f is a distance preserving map. Show that an isometry, f: R2 R2 also preserves angles. In other words if two line segments meeting at a point determine an angle a, their image line segments meeting at the image of that point also determine the angle a.
Transcribed Image Text:(3) Recall that a map, f: R2 R2, is an isometry if |P - Q| = |ƒ(P) − f(Q)| for all pairs of points P and Q in R². Thus, f is a distance preserving map. Show that an isometry, f: R2 R2 also preserves angles. In other words if two line segments meeting at a point determine an angle a, their image line segments meeting at the image of that point also determine the angle a.
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