Chapter 14.3, Problem 6CE

To determine

To find: $T:(x,y)\to (?,?)$

Answer to Problem 6CE

  $T(x,y)\to (x,y-4)$

Explanation of Solution

Given information :

Diagram shows a point $P$ on the coordinate plane & it’s image $P\text{'}$ under a transition: $T(P)\to P\text{'}$

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

  $T(P)\to P\text{'}$

As we see in graph, point $P$ moves right by 5 unit & then move up by 3 units to reach the point $P\text{'}$ .

  $\begin{array}{l}\therefore P=(x,y)\\ T(P)\to P\text{'}\\ T(x,y)\to (x,y-4)=P\text{'}\end{array}$

Hence,

  $T(x,y)\to (x,y-4)$