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.
