Chapter 5.1, Problem 55PPE

To determine

To show: the points are on the same line.

Answer to Problem 55PPE

The three points are does not lie on the same line.

Explanation of Solution

Given information:

Consider the points $S(-3,4),T(0,2)$ and $X(-3,0)$ .

Calculation:

Slope of the line TX and ST must be the same for three points on the same line.

Since, the slope of the line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

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

To find the slope of the line $ST:$

By substituting $S(-3,4)$ for $\left(x_1,y_1\right)$ and $T(0,2)$ for $\left(x_2,y_2\right)$

  $\begin{array}{l}\text{Slope}=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{2-4}{0+3}\\ =\frac{-2}{3}\\ =-\frac{2}{3}\end{array}$

So, the slope of the line $ST$ = $-\frac{2}{3}$

To find the slope of the line $TX:$

By substituting $T(0,2)$ for $\left(x_1,y_1\right)$ and $X(-3,0)$ for $\left(x_2,y_2\right)$

  $\begin{array}{l}\text{Slope}=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{0-2}{-3-0}\\ =\frac{-2}{-3}\\ =\frac{2}{3}\end{array}$

So, the slope of the line $TX=\frac{2}{3}$

Hence the slope of the line $ST$ is not same as the slope of the line $TX$

Therefore, the three points are does not lie on the same line.