How did they get the answer

The question reads: Determine whether triangle ABC is a right triangle for the given vertices. Explain.
A(2, 7), B(3, 6), C(-4, -1).
The answer is "YES, this is a right triangle."
But HOW do you get the answer? And they didn't explain! So please explain the steps if you don't mind. Thanks!

Find the equation of the three lines, and look at the slopes. (you should know how to find a line given two points)

(I should emphasize that finding just the slopes is all that is necessary for this) (y1-y2)/(x1-x2) for the three possible pairs of points

y = x + 3
y = -x + 9
y = (4/3)x + (13/3)

two lines have negative inverse slopes, which means they are perpendicular to each other (coming together at a right angle) and since they all share a common point it indicates a right triangle.

There are two ways to prove it is a right triangle:

1) find the lengths of the sides, using distance formula. Then show that the pythagorean relationship exists: a^2+b^2= c^2

AB= sqr(2), BC= sqr(98); AC= sqr(100)
So [sqr(2)]^2 + [sqr(98)]^2= [sqr(100)]^2
2+98=100

Or
2) find the slopes of the three sides. If two sides are perpendicular, it is a right triangle. (the slopes will be negative reciprocals)

m(AB)= (6-7)/(3-2)= -1
m(BC)= (-1-6)/(-4-3)= +1
m(AC)= (-1-7)/(-4-2)= 8/6=4/3
so sideAB and side BC are perpendicular.

Hoping this helps!

A right angle triangle has the property a squared +b squared = c squared.
Length of side a =square root of (rise squared +run squared)
a squared =(6--1) squared +(3--4) squared =49+49
etc