Chapter 11.8, Problem 23STP

To determine

To find:Which series of transformations maps $ABCD$ onto $PQRS$ .

Answer to Problem 23STP

Translation then a Dilation.

Explanation of Solution

From given figure

We can say that

First Figure $ABCD$ is translated four units down and the dilated using a scale factor.

We can find scale factor by dividing any side of the image polygon by corresponding side of Original polygon.

Given $ABCD$ is Original polygon

From given figure we can say that

  $AB=4$

Given $PQRS$ is image polygon

From given figure we can say that

  $PQ=2$

Therefore,

Scale factor $=\frac{PQ}{AB}$

  $\Rightarrow$ Scale factor $=\frac{2}{4}$

  $\Rightarrow$ Scale factor $=\frac{1}{2}$

Therefore,

  $ABCD$ is translated four units down and the dilated using a scale factor of $k=\frac{1}{2}$