Question

On a coordinate plane, triangle A B C is shown. Point A is at (negative 2, negative 4), point B is at (2, negative 1), and point C is at (3, negative 4).
Triangle ABC is an isosceles triangle in which side
AB = AC. What is the perimeter of triangle ABC?

5 + StartRoot 10 EndRoot units
10 + StartRoot 10 EndRoot units
10 StartRoot 10 EndRoot units
50 units

Answer 1

Compute the side lengths:
- AB = distance between (-2,-4) and (2,-1): sqrt(4^2+3^2) = 5
- AC = distance between (-2,-4) and (3,-4): sqrt(5^2+0^2) = 5
- BC = distance between (2,-1) and (3,-4): sqrt(1^2+3^2) = sqrt(10)

Perimeter = AB + AC + BC = 5 + 5 + sqrt(10) = 10 + sqrt(10) units.