Question

a set of plans for a new bandstand includes a triangular support. the coordinates of the triangle on the plans are a(2, - 3), b(0, - 2) and c(-2, - 6). which statement classifies the triangle by angles? since the slope of $overline{ab}$ is $-\frac{1}{2}$ and the slope of $overline{bc}$ is 2, the triangle is an acute triangle. since the slope of $overline{bc}$ is 2 and the slope of $overline{ac}$ is $\frac{3}{4}$, the triangle is a right triangle. since the slope of $overline{ab}$ is $-\frac{1}{2}$ and the slope of $overline{bc}$ is 2, the triangle is a right triangle. since the slope of $overline{bc}$ is 2 and the slope of $overline{ac}$ is $\frac{3}{4}$, the triangle is an acute triangle.

Explanation:

Step1: Recall slope - perpendicularity relationship

If the product of the slopes of two lines is - 1, the lines are perpendicular.

Step2: Calculate the product of slopes of AB and BC

The slope of $\overline{AB}$ is $-\frac{1}{2}$ and the slope of $\overline{BC}$ is 2. The product of their slopes is $-\frac{1}{2}\times2=- 1$.

Step3: Determine the type of triangle

Since two sides of the triangle (AB and BC) are perpendicular, the triangle is a right - triangle.

Answer:

Since the slope of $\overline{AB}$ is $-\frac{1}{2}$ and the slope of $\overline{BC}$ is 2, the triangle is a right triangle.