Chapter 11.8, Problem 14IP

To determine

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

Answer to Problem 14IP

It means $\Delta ABC$ is translated $1$ unit to the right and $1$ unit down followed by a dilation with a scale factor of $k=4$ to get Rectangle $A\text{'}B\text{'}C\text{'}$

Explanation of Solution

From Given figure

We get

From $\Delta ABC$

  $AC=2$

From Rectangle $A\text{'}B\text{'}C\text{'}$

  $A\text{'}C\text{'}=8$

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

  $\frac{A\text{'}C\text{'}}{AC}=\frac{8}{2}=4$

It means

Scale factor $=k=4$

From given figure

We can say that

Translation of $1$ unit to the right and $1$ unit down occurs to get the image.

It means $\Delta ABC$ is translated $1$ unit to the right and $1$ unit down followed by a dilation with a scale factor of $k=4$ to get Rectangle $A\text{'}B\text{'}C\text{'}$