Question

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

Answer 1

Answer:

See below

Step-by-step 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 = $\sqrt{(9-3)^2+(2-(-1))^2} = \sqrt{6^2+3^2} = \sqrt{45} = 3\sqrt{5}$
• BC = $\sqrt{(6-9)^2 + (-4-2)^2} = \sqrt{3^2 + (-6)^2} = \sqrt{45} = 3\sqrt{5}$

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