Geometry question

Question

Prove that the triangle whose coordinates are A(3,2);B(10,3) ; C(6, 6) is isosceles.

Answer 1

In an isosceles triangle, two of the three sides are equal in length. Use the distance formula between two points:

distance = √( (x₂-x₁)²+(y₂-y₁)² )

to find the distance between A and B, then B and C, then C and A. These are the three sides of the triangle. If two of the three sides, but not all three, are the same length, the triangle is isosceles.

Answer 2

AB^2 = 1+49 = 50

BC^2 = 9+16 = 25

AC^2 =9+16 = 25

BC =AC = 5, two sides have the same length, that's the definition of an isosceles triangle.