Question

Prove that triangle ABC is Isosceles, given the following points.

A (3, -1)


B (9, 2)


C (6, -4)

Answer 1

See below

Explanation:

Given points:

• A (3, -1) , B (9, 2) , C (6, -4)

First, plot the points on the coordinate plane (see attached)

We see that AB and BC look the same. Let's find their length:

• AB =
  `√((9-3)^2+(2-(-1))^2) = √(6^2+3^2) = √(45) = 3√(5)`
• BC =
  `√((6-9)^2 + (-4-2)^2) = √(3^2 + (-6)^2) = √(45) = 3√(5)`

We showed that AB = BC = 3√5, so the triangle has two sided of the same length, therefore is isosceles.