Chapter 14.3, Problem 5WE

To determine

To find: $T:(?,?)\to (0,0)$ .

Answer to Problem 5WE

  $T:(-4,-3)\to (0,0)$

Explanation of Solution

Given information :

Translation $T:(-2,3)\to (2,6)$

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 $T:(-2,3)\to (2,6)$

  $\begin{array}{l}T(-2,3)\to (2,6)=(-2+4,3+3)\\ \therefore T(x,y)\to (x+4,y+3)\\ \therefore T^{-1}(x,y)\to (x-4,y-3)\\ \Rightarrow T^{-1}(0,0)\to (0-4,0-3)=(-4,-3)\\ \Rightarrow T(-4,-3)\to (0,0)\end{array}$

Hence,

The preimage of $(0,0)$ is $(-4,-3)$ .