Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.6 - The Rectangular Coordinate System and Graphs - Exercises - Page 58: 25

Answer

Right triangle

Work Step by Step

Determine the length of each side using the formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, where $(x_1,y_1),(x_2,y_2)$ are the coordinates of the two points. $d_1=\sqrt{(4-2)^2+(0-1)^2}=\sqrt 5$ $d_2=\sqrt{[4-(-1)]^2+[0-(-5)]^2}=\sqrt{50}=5\sqrt 2$ $d_3=\sqrt{[2-(-1)]^2+[1-(-5)]^2}=\sqrt{45}=3\sqrt 5$ Compute $d_1^2+d_3^2$: $d_1^2+d_3^2=(\sqrt 5)^2+(3\sqrt 5)^2=5+45=50$ Compute $d_2^2$: $d_2^2=(5\sqrt 2)^2=50$ As $d_1^2+d_3^2=d_2^2$, the three sides verify the Pythagorean Theorem, so the triangle is a right triangle.
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