Explain how slope is used to determine if a triangle is a right triangle.

Do determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals.

You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle.

Let's say there's triangle ABC.

If the slope of AB is 1/2

and the slope of BC is 2/5

and the slope of CA is - 2/1

then AB and CA intersect resulting in a right angle (triangle).

A right triangle contains a right angle, so it must have two sides that are perpendicular. If the slopes of two sides can be shown to be negative reciprocals of each other, then it can be concluded that a right angle is formed. If a triangle contains a right angle, then it is a right triangle.