Chapter 14.3, Problem 2CE

To determine

To find: Image of $(4,6)$ and the preimage of $(2,3)$ .

Answer to Problem 2CE

The image of $(4,6)$ is $(-1,10)$ and preimage of $(2,3)$ is $(7,-1)$ .

Explanation of Solution

Given information :

Translation $T:(x,y)\to (x-5,y+4)$

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 $T:(x,y)\to (x-5,y+4)$

  $T(4,6)\to (4-5,6+4)=(-1,10)$

  $T^{-1}(x,y)\to (x+5,y-4)$

  $T^{-1}(2,3)\to (2+5,3-4)=(7,-1)$

Hence,

The image of $(4,6)$ is $(-1,10)$ and preimage of $(2,3)$ is $(7,-1)$ .