The vertices of a triangle are listed below.
q(-3,7), r(8,7), s(-6,-5)
which of the following correctly classifies the triangle?

This question is a bit tedious. In order to answer it, we will have to find the distance between each vertex using the distance formula.

d² = (x - x)² + (y - y)²   Distance Formula
d² = (-3 - 8)² + (7 - 7)²   Substitute for points Q (-3,7) and R (8,7)
d² = -11² + 0²   Collect like terms
d² = 121   Square
d = 11   Take the square root of both sides to cancel out the exponent on the left

The distance between points Q and R is 11. Now let's use the formula on the rest of the points.

R and S

d² = (8 + 6)² + (7 + 5)²   Keep in mind that when you subtract a negative, it becomes a positive.
d² = 196 + 144
d² = 340
d = 18.4

Q and S

d = 12.4

This is scalene triangle, because none of the sides are equal. I was a bit rushed on this one, so you might want to check my math.