Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.2 - The Rectangular Coordinate System - 1.2 Problem Set - Page 26: 94

Answer

$$a^2+b^2=(3)^2+(4)^2 = 25\\c^2 = (5)^2=25$$ $\therefore a^2+b^2 = c^2 $ and the triangle is a right triangle.

Work Step by Step

To find $a,b$ and $c$, we use the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\a=\sqrt{(-3-0)^2+(2-2)^2}=3\\b=\sqrt{(-3-(-3))^2+(-2-2)^2}=4\\ c=\sqrt{(-3-0)^2+(-2-2)^2}=5$$ $$a^2+b^2=(3)^2+(4)^2 = 25\\c^2 = (5)^2=25$$ $\therefore a^2+b^2 = c^2 $ and the triangle is a right triangle.
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