Chapter 14.3, Problem 7CE

To determine

To find:Preimage of origin.

Answer to Problem 7CE

The preimage of origin $(0,0)$ , $T^{-1}:(0,0)\to (-5,-7)$

Explanation of Solution

Given information :

Translation, image of origin is $(5,7)$ .

  $T:(0,0)\to (5,7)$

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

  $T:(0,0)\to (5,7)$

As we see in graph, point $P$ moves right by 5 unit & then move up by 7 units to reach the point $P\text{'}$ .

  $\begin{array}{l}T:(P)\to P\text{'}\\ T:(0,0)\to (5,7)\\ \Rightarrow T:(x,y)\to (x+5,y+7)\\ \Rightarrow T^{-1}:(x,y)\to (x-5,y-7)\\ \Rightarrow T^{-1}:(0,0)\to (0-5,0-7)=(-5,-7)\end{array}$

Hence,

Preimage of origin, $T^{-1}:(0,0)\to (-5,-7)$