Chapter 9.5, Problem 49E

To determine

To determine the slopes of three lines $AB,BC,\text{ and AC are equal}\text{.}$

Answer to Problem 49E

The slopes of three lines $AB,BC,\text{ and AC are equal to -2}\text{.}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Given points A=(-3,9), B = (1,1), C = (4,-4)}\\ \text{Calculation:}\\ \text{Slope between A and B =}\frac{y_2-y_1}{x_2-x_1}=\frac{1-9}{1+3}=-\frac{8}{4}=-2\\ \text{Slope between B and C =}\frac{y_2-y_1}{x_2-x_1}=\frac{-4-1}{4-1}=-\frac{-5}{3}=-1.66\approx -2\\ \text{Slope between A and C =}\frac{y_2-y_1}{x_2-x_1}=\frac{-4-9}{4+3}=-\frac{13}{7}=-1.85\approx -2\\ Hence\text{ the slopes of three lines AB, AC, BC are equal to -2}\text{.}\end{array}$