Chapter 4.3, Problem 31E

To determine

To find: the lines from the right angle or not.

Answer to Problem 31E

Therefore, the angle between the two lines is not right angle.

Explanation of Solution

Given:

Consider the line L1 passing through $\left(-4,16\right)$ and $\left(0,8\right)$ and L2 passing through $\left(0,8\right)$ and $\left(-4,0\right)$ .

The objective is to check whether the lines form the right angle or not.

Calculation:

Find the slope of the line L1 as follows:

The slope of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Therefore, the slope of the line $\left(-4,16\right)$ and $\left(0,8\right)$

  $m_1=\frac{8-16}{0-\left(-4\right)}$

  $m_1=-2$

Find the slope of the line L2 as follows:

The slope of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Therefore, the slope of the line $\left(0,8\right)$ and $\left(-4,0\right)$

  $m_2=\frac{0-8}{\left(-4\right)-0}$

  $m_2=2$

The product of slope $m_1{m}_2=-4$

That is, $m_1{m}_2\text{'}-1$

Since their slopes are not negative reciprocals of each other, therefore, the angle between the two lines is not right angle.

Conclusion:

Therefore, the angle between the two lines is not right angle.