Exercise 9 Page 643

To draw a rotation of a figure about point $K,$ we need to follow a few steps.

1. Draw a segment from one of the vertices to point $K.$
2. Draw the given angle of rotation using the segment from Step $1$ and a protractor.
3. Use a ruler to draw the image of the chosen vertex. Make sure that the segment from point $K$ to the image has the same length as the segment from Step $1.$
4. Repeat Steps $1\text{-}3$ for the remaining vertices and connect the rotated points.

Let's draw the rotation of the given figure!

Step $1$

Notice that in this case point $K$ is one of the vertices of the given figure. Therefore, the image and the preimage are the same for point $K.$ Let's begin by drawing a segment from $R$ to $K.$

Step $2$

Now we will draw the angle of rotation. In this case, it is $260^{\circ }.$ Since it is greater than $180,$ we cannot do it immediately with a protractor. Let's extend $\overline{KR}$ first. This gives us a $180^{\circ }$ angle.

Next, we will determine the remaining angle that we need to draw. We can use a protractor to draw an $80^{\circ }$ angle.

Step $3$

Finally, we will use a ruler to draw the image of $R.$ We will measure $\overline{KR},$ then draw $\overline{K{R}^{\prime }}$ such that $K{R}^{\prime }=KR.$

Step $4$

We repeat Steps $1\text{-}3$ for the remaining vertices.

Finally, we can connect the points to form the rotated image.