Q. 111 - Precalculus Enhanced with Graphing Utilities

Question

Use slopes to show that the triangle whose

vertices are $(-2,5), (1,3)$ and $(-1,0)$ is a right triangle.

Step-by-Step Solution

Answer

The given vertices form a right triangle.

Step 1. Given information

Three points that are vertices of a triangle are given: $(-2,5), (1,3)$ and $(-1,0)$

Step 2. Required to find

Show that the given vertices form a right triangle. 

Step 3. Finding slopes of sides of triangle

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Slope of line joining $(-2,5)$ and $(1,3)$ is: $m_1=\frac{3-5}{1-(-2)}$

$m_1=-\frac{2}{3}$

Slope of line joining $(1,3)$ and $(-1,0)$ is: $m_2=\frac{0-3}{-1-1}$

$m_2=\frac{3}{2}$

Step 4. Checking whether sides are perpendicular lines

Above two lines that form the sides of the triangle are perpendicular as product of their slopes is $-1$.

$m_1\times m_2=-\frac{2}{3}\times \frac{3}{2}=-1$

Therefore, the given vertices form right triangle.