Chapter 12.4, Problem 4E

To determine

To describe:The translation of the given figure in words.

Answer to Problem 4E

Each point or vertex of the figure $\text{DEFG}$ is to be moved $5$ units to the rightalong x-axis and $\text{4}$ units upalong y-axis to reach figure $\text{D'E'F'G'}$ .

Explanation of Solution

Given information :

Consider the graph provided in the question:

As per the problem

The figure $\text{DEFG}$ is the original figure and $\text{D'E'F'G'}$ is the image of $\text{DEFG}$ .

In a translation, a figure and its image are congruent.

Describing translation of figure $\text{DEFG}$ to $\text{D'E'F'G'}$ :

Think of moving horizontallyalong x-axis and verticallyalong y-axis from a point on the original figure to the corresponding point on the new figure.

For point $\text{D(-4,-4)}$ , move $5$ units to the right along x-axis and $3$ units up along y-axis to reach $\text{D'(1,-1)}$ .

For point $\text{E(-3,-2)}$ , move $5$ units to the right along x-axis and $3$ units up along y-axis to reach $\text{E'(2,1)}$ .

For point $\text{F(-1,-2)}$ , move $5$ units to the right along x-axis and $3$ units up along y-axis to reach $\text{F'(4,1)}$ .

For point $\text{G(-1,-4)}$ , move $5$ units to the right along x-axis and $3$ units up along y-axis to reach $\text{G'(4,-1)}$ .

The transition of each point of figure $\text{DEFG}$ written using coordinate notation:

  $(x,y)\to (x+5,y+3)$

That is,

Each point or vertex of the figure $\text{DEFG}$ is to be moved $5$ units to the rightalong x-axis and $\text{4}$ units upalong y-axis to reach figure $\text{D'E'F'G'}$ .