Chapter 12.4, Problem 23E

To determine

To describe the translation

Answer to Problem 23E

The translation is $(x,y)\to (x+5.5,y+4.5)$

Explanation of Solution

Given information:

  $\begin{array}{l}\text{A}=(x1,y2)=(-6,-4)\\ \text{B}=(x2,y2)=(5,5)\end{array}$

Calculation :

Evaluate M the midpoint of A and B:

  $\begin{array}{l}M=\frac{(x1+x2}{2},\frac{y1+y2)}{2}\\ \text{substituting values:}\\ \text{M=}\left(\frac{-6+5}{2},\frac{-4+5}{2}\right)\\ \text{Evaluate:}\\ \text{M=(}-0.5,0.5)\end{array}$

In order to determine the constants of the translation, let us form an equation:

  $\begin{array}{l}(x1+a,y1+b)=(x,y)\\ {\text{Here P}}_1=\text{A and (}x,y)=M,\text{ so substitute values:}\\ \text{Solve for }a:\\ a=6-0.5=5.5\\ \text{Solve for }b:\\ b=4+0.5=4.5\end{array}$

Therefore

The required translation is $(x,y)\to (x+5.5,y+4.5)$