Chapter 14.3, Problem 6WE

To determine

To find:Preimage of $P$ .

Answer to Problem 6WE

The preimage of $P$ is $(-7,3)$ .

Explanation of Solution

Given information :

The image of $P(-1,5)$ under a translation is $P\text{'}(5,7)$ .

Translation $T:(-1,5)\to (5,7)$

Concept used:

A translation moves ("slides") an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it.The original object is called the pre-image, and the translation is called the image.

As per the given problem

Translation $T:(-1,5)\to (5,7)$

  $\begin{array}{l}T(-1,5)\to (5,7)=(-1+6,5+2)\\ \therefore T(x,y)\to (x+6,y+2)\\ \therefore T^{-1}(x,y)\to (x-6,y-2)\\ \Rightarrow T^{-1}(-1,5)\to (-1-6,5-2)=(-7,3)\\ \Rightarrow T(-7,3)\to (-1,5)\end{array}$

Hence,

The preimage of $P$ is $(-7,3)$ .