Question

Prove (0,0) (5,5) (-5,5) are the values of a right isosceles triangle.

Answer 1

Step-by-step explanation:

Let,

A(0,0)

B(5,5)

C(-5,5)

Now,

AB²=(5-0)²+(5-0)²

AB²=25+25

AB²=50

AC²=(-5-0)²+(5-0)²

     =25+25

AC²=50

BC²=(-5-5)²+(5-5)²

     =100+0

     =100

Now,

AB²=AC²

AB=AC

Thus ΔABC is a isosceles triangle.

Also,

AB²+AC²=BC²

Thus by the converse of Pythagoras Theorem,

ΔABC is a right triangle right-angled at B

∴ΔABC is a right isosceles triangle