Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 10 - Section 10.1 - The Rectangular Coordinate System - Exercises: 25c

Answer

isosceles triangle.

Work Step by Step

G(-5,2) H(-2,6) and K(2,3) Using distance formula x1=-5,y1=2,x2=-2,y2=6 then, $\overline{GH}$ = $\sqrt (x2-x1)^{2} + (y2-y1)^{2}$ = $\sqrt (-2+5)^{2} + (6-2)^{2}$ =5 units Similarly, $\overline{HK}$ = $\sqrt (2-(-2))^{2} + (3-6)^{2}$ =$\sqrt 4^{2} + (-3)^{2}$ = $\sqrt 16+9$ = $\sqrt 25$ =5 units $\overline{KG}$ = $\sqrt (2-(-5))^{2} + (3-2)^{2}$ =$\sqrt 7^{2} + 1^{2}$ = $\sqrt 49+1$ = $\sqrt 50$ units Therefore $\overline{GH}$ = $\overline{HK}$ in triangle GHK therefore triangle GHK is isosceles triangle.
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