Chapter 9.3, Problem 28PPS

To determine

To rotate: The line by given degree and find the equation of the resulting image.

Answer to Problem 28PPS

The equation of image about the x intercept is $y=-x+5$ and about the y intercept is $y=-x-5$ .

Explanation of Solution

Consider the line.

  $y=x-5$

The x intercept of the line is,

  $\begin{array}{c}0=x-5\\ x=5\end{array}$

Rotate the given line about the point $\left(5,0\right)$ through $90°$ .

The image will be perpendicular to the line with same x intercept.

Thus, the equation of line is,

  $y=-x+5$

The y intercept of the line is,

  $\begin{array}{c}y=0-5\\ x=-5\end{array}$

Rotate the given line about the point $\left(0,-5\right)$ through $90°$ .

The image will be perpendicular to the line with same y intercept.

Thus, the equation of line is,

  $y=-x-5$

Therefore, the equation of image about the x intercept is $y=-x+5$ and about the y intercept is $y=-x-5$ .