Chapter 12.4, Problem 4C

To determine

To showthe given translations are different.

Answer to Problem 4C

The transition of a point using coordinate notation:

  $(x,y)\to (x+3,y+2)$

Means,

The point moves $3$ units to the right along x-axis and $2$ units up along y-axis to reach image point.

Whereas,

The transition of a point using coordinate notation:

  $(x,y)\to (x-3,y+2)$

Means,

The point moves $3$ units to the left along x-axis and $2$ units up along y-axis to reach image point.

Explanation of Solution

Given information :

Consider the coordinate notations provided in the question:

  $(x,y)\to (x+3,y+2)$

And, $(x,y)\to (x-3,y+2)$

Concept used:The translation of a point $(x,y)$ can be described using coordinate notation:

  $(x,y)\to (x+a,y+b)$

Where $a$ indicates how many units a point moves horizontally and $b$ indicates how many units a point moves vertically. Move the point $(x,y)$ to the right if $a$ is positive and to the left if $a$ is negative. Move the point up if $b$ is positive and down if $b$ is negative.

As per the problem

The translation of a point $(x,y)$ can be described using coordinate notation:

  $(x,y)\to (x+a,y+b)$

Where $a$ indicates how many units a point moves horizontally and $b$ indicates how many units a point moves vertically. Move the point $(x,y)$ to the right if $a$ is positive and to the left if $a$ is negative. Move the point up if $b$ is positive and down if $b$ is negative.

Therefore,

The transition of a point using coordinate notation:

  $(x,y)\to (x+3,y+2)$

Here $a$ = $3$ and $b$ = $2$ .

Means,

The point moves $3$ units to the right along x-axis and $2$ units up along y-axis to reach image point.

Whereas,

The transition of a point using coordinate notation:

  $(x,y)\to (x-3,y+2)$

Here $a$ = $-3$ and $b$ = $2$ .

Means,

The point moves $3$ units to the left along x-axis and $2$ units up along y-axis to reach image point.