Question

Help please: Use the distance formula to show that the triangle ABC, with vertices A(-1,-2),B(3,2), and C(1,4), is a right triangle. Explain your reasoning.

Answer 1

AB(4; 4)
BC(-2; 2)
AC(2; 6)

Length of AB = sqrt(4^2 + 4^2) = sqrt(32) = 4sqrt(2)
Length of BC = sqrt(-2^2 + 2^2) = sqrt(8) = 2sqrt(2)
Length of AC = sqrt(2^2 + 6^2) = sqrt(40) = 2sqrt(10)

According to pythagoras a^2 + b^2 = c^2 if it's a right triangle.

4sqrt(2) + 2sqrt(2) = 2sqrt(10)
32 + 8 = 40

And that is true.

Win.

Answer 2

Thank you. So basically, you find the distance between AB,BC, and AC. Then you plug it in the a2+b2=c2 formula?

Answer 3

Since you can only use the distances I can't really see another way. So yeah, 'a^2 + b^2 = c^2 must be true for right triangles' is basically all you need to explain imo : )

Answer 4

okay, thanks.