Chapter 9.4, Problem 41HP

To determine

To find: Whether the order of the reflection affects the final image if the image is reflected in $y=x$ .

Answer to Problem 41HP

The order is affected if the segments with the end points are to be reflected at the end points.

Explanation of Solution

Consider that if the segments with the end points are to be reflected at the end points then, $\left(a,b\right)$ and $\left(c,d\right)$ are to be reflected about the x axis and the coordinate of the end point of the reflected image are $\left(a,-b\right),\left(c,-d\right)$ . When the segment is reflected about the line $y=x$ . Then, the coordinates of the end points of the final image are $\left(-b,a\right)$ and $\left(-d,c\right)$ as shown in Figure 1

  

Figure 1

Consider that when the original image is reflected about the x axis. Then, the coordinates of the end points of the reflected image are $\left(b,a\right)$ and $\left(d,c\right)$ . If the segment is then reflected about the x axis, then the coordinates of the end points of the final image are $\left(b,-a\right)$ and $\left(d,-c\right)$ as shown in Figure 2

  

Figure 2