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+ Recall that a map, f: R2 R², is an isometry if |P-Q| = |ƒ(P) — ƒ (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.

+ Recall that a map, f: R2 R², is an isometry if |P-Q| = |ƒ(P) — ƒ (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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
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+ Recall that a map, f: R2 R², is an isometry if |P-Q| = |ƒ(P) — ƒ (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:+ Recall that a map, f: R2 R², is an isometry if |P-Q| = |ƒ(P) — ƒ (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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