Three points determine an isosceles triangle: Show that these points determine an isosceles triangle: (-2, 5); (-5, 1); (-1, -2).

We need the lengths of the 3 sides of the triangle. If it is an isosceles triangle, just 2 of the lengths will be equal. We can use the Distance Formula on the 3 pairs of points:

For (-2,5) and (-5,1), the length is

For (-5,1) and (-1, -2), the length is

For (-2, 5) and (-1, -2), the length is

Since d₁ = d₂ and d₃ is different and less than d₁ + d₂,

the triangle is isosceles.