Answer
Isosceles Triangle
Work Step by Step
A(0,0) B (4,0) and C(2,5)
Using distance formula
x1=0,y1=0,x2=4,y2=0
then, $\overline{AB}$ = $\sqrt (x2-x1)^{2} + (y2-y1)^{2}$
= $\sqrt (4-0)^{2} + (0-0)^{2}$
=4 units
Similarly,
$\overline{BC}$ = $\sqrt (2-4)^{2} + (5-0)^{2}$
=$\sqrt 2^{2} + 5^{2}$ = $\sqrt 4+25$ = $\sqrt 29$
$\overline{CA}$ = $\sqrt (2-0)^{2} + (5-0)^{2}$
=$\sqrt 2^{2} + 5^{2}$ = $\sqrt 4+25$ = $\sqrt 29$
Therefore $\overline{BC}$ = $\overline{CA}$ in triangle ABC
therefore triangle ABC is isosceles.
