Question

A(-3,-4),B(2,6),C(-6,10) whether the points are vertices of the right triangle?

Answer 1

AB²= (-3-2)²+(-4-6)²
= 25+100
=125 units.
BC²= (2+6)²+(6-10)²
=64+16
=80 units.
AC²=(-3+6)²+(-4--10)²
=9+196
=205 units.
If it is a right triangle, AB²+BC²=AC².
But, here, 80+125=205.
=205.
Therefore, these are the vertices of a right triangle.

Thank you.