Chapter 12.4, Problem 2C

To determine

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

Answer to Problem 2C

Each point or vertex of the figure $\text{DEFG}$ is to be moved $\text{6}$ units to the left along x-axis and $\text{4}$ units down along 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 quadrilateral $\text{DEFG}$ to $\text{D'E'F'G'}$ :

Think of moving horizontally along x-axisand verticallyalong y-axis from a point on the original figure to the corresponding point on the new figure.

For point $\text{D(2,1)}$ , move $\text{6}$ units to the left along x-axisand $\text{4}$ units down along y-axisto reach $\text{D'(-4,-3)}$ .

For point $\text{E(3,3)}$ , move $\text{6}$ units to the leftalong x-axis and $\text{4}$ units down along y-axisto reach $\text{E'(-3,-1)}$ .

For point $\text{F(4,3)}$ , move $\text{6}$ units to the leftalong x-axis and $\text{4}$ units down along y-axisto reach $\text{F'(-2,-1)}$ .

For point $\text{G(3,1)}$ , move $\text{6}$ units to the leftalong x-axis and $\text{4}$ units downalong y-axis to reach $\text{G'(-3,-3)}$ .

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

  $(x,y)\to (x-6,y-4)$

That is,

Each point or vertex of the figure $\text{DEFG}$ is to be moved $\text{6}$ units to the leftalong x-axis and $\text{4}$ units down along y-axis to reach figure $\text{D'E'F'G'}$ .