Chapter 12.4, Problem 7E

To determine

To describe: The given translation.

Answer to Problem 7E

The translation is made using the following coordinate notation:

  $(x,y)\to (x+(-5),y+0)$

Explanation of Solution

Given information:

The following translation:

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

$(x,y)\to (x+a,y+b)$

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

In the above translation, $a$ is $-5$ and $b$ is $0$ . The image has moved $5$ units to the left of the original figure, hence $a$ is $-5$ but has not moved up or down with respect to the original figure, hence $b$ is $0$ .

To verify the values of $a$ and $b$ , substitute their values in the above coordinate notation:

$\begin{array}{l}\text{D(2,-3)}\to \text{D(2-5,-3+0)}\to \text{D'(-3,-3)}\\ \text{E(3,1)}\to \text{E(3-5,1+0)}\to \text{E'(-2,1)}\\ \text{F(4,-1)}\to \text{F(4-5,-1+0)}\to \text{F'(-1,-1)}\\ \text{G(4,-4)}\to \text{G(4-5,-4+0)}\to \text{G'(-1,-4)}\end{array}$