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Describing Triangles

Describing Triangles 1.9 - Solution

arrow_back Return to Describing Triangles

Let's start by drawing the triangle in a coordinate plane.

Classify by Sides

To classify a triangle by its sides means to classify it as either scalene, isosceles, or equilateral. To do that we have to calculate the length of all sides using the distance formula. Let's begin by finding the distance between and This will give us
Evaluate right-hand side
The length of is We can find the rest of the sides using the same method.
Side Points Length

As we can see, each side of the triangle has a different length, so is a scalene triangle.

Right Triangle?

In our diagram, we see that and are acute angles. Therefore, if is a right triangle, the right angle must be To determine if this is the case, we will first calculate the slope of and by using the Slope Formula.

Side Points Slope Simplified Slope

Since and are not opposite reciprocals, is not perpendicular to Therefore, is not a right triangle.