Chapter 11.8, Problem 13IP

To determine

To find: Determine a sequence of transformations that maps the preimage onto the image.

Answer to Problem 13IP

It means rectangle $JKLM$ is Reflected over the x-axis followed by a dilation with a scale factor of $k=2$ to get Rectangle $J\text{'}K\text{'}L\text{'}M\text{'}$

Explanation of Solution

From Given figure

We get

From Rectangle $JKLM$

  $\begin{array}{l}JK=3\\ KL=2\\ LM=3\\ ML=2\end{array}$

From Rectangle $J\text{'}K\text{'}L\text{'}M\text{'}$

  $\begin{array}{l}J\text{'}K\text{'}=6\\ K\text{'}L\text{'}=4\\ L\text{'}M\text{'}=6\\ M\text{'}J\text{'}=4\end{array}$

If two polygons are similar then the ratio of the lengths of the two corresponding sides is the scale factor.

From given figure we can say that there is Reflection of Rectangle $JKLM$ over x-axis has occurred

Given both rectangles are Similar. It means Ratio of length of each side are Similar

Ratio of lengths of each side are

  $\frac{J\text{'}K\text{'}}{JK}=\frac{K\text{'}L\text{'}}{KL}=\frac{L\text{'}M\text{'}}{LM}=\frac{M\text{'}J\text{'}}{ML}=2$

It means rectangle $JKLM$ is Reflected over the x-axis followed by a dilation with a scale factor of $k=2$ to get Rectangle $J\text{'}K\text{'}L\text{'}M\text{'}$