Chapter 14.8, Problem 4ST2

To determine

To complete the statement.

Answer to Problem 4ST2

  $D_{o,\frac{1}{2}}\circ D_{R,\frac{1}{2}}:P\to$ P

Explanation of Solution

Given information:

The given statement is $D_{o,\frac{1}{2}}\circ D_{R,\frac{1}{2}}:P\to$ _____

Coordinate of R is $\left(0,-3\right)$

$\begin{array}{l}RP\text{'}=\frac{1}{2}RP\\ RP\text{'}=\frac{1}{2}\times 2\left[RP=2,\text{from figure}\right]\\ RP\text{'}=1\end{array}$

Therefore P’ maps at Q .

The dilation $D_{R,\frac{1}{2}}:P$ maps at Q .

Since O is at the origin.

$\begin{array}{l}OQ\text{'}=\frac{1}{2}OQ\\ OQ\text{'}=\frac{1}{2}\times 2\left[PQ=2,\text{from figure}\right]\\ OQ\text{'}=1\end{array}$

The dilation $D_{o,\frac{1}{2}}:Q$ maps at P .

Therefore,

The dilation $D_{o,\frac{1}{2}}\circ D_{R,\frac{1}{2}}:P\to$ P