Chapter 12.4, Problem 1C

To determine

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

Answer to Problem 1C

Each point or vertex of the figure $\text{ABC}$ is to be moved $\text{4}$ units to the rightalong x-axis and $3$ units downalong y-axis to reach figure $\text{A'B'C'}$ .

Explanation of Solution

Given information :

Consider the graph provided in the question:

As per the problem

The figure $\text{ABC}$ is the original figure and $\text{A'B'C'}$ is the image of $\text{ABC}$ .

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

Describing translation oftriangle $\text{ABC}$ to triangle $\text{A'B'C'}$ :

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 $\text{A(-4,1)}$ , move $\text{4}$ units to the right along x-axis and $3$ units downalong y-axis to reach $\text{A'(0,-2)}$ .

For point $\text{B(-1,3)}$ , move $\text{4}$ units to the right along x-axis and $3$ units downalong y-axis to reach $\text{B'(3,0)}$ .

For point $\text{C(-1,1)}$ , move $\text{4}$ units to the rightalong x-axis and $3$ units downalong y-axis to reach $\text{C'(3,-2)}$ .

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

  $(x,y)\to (x+4,y-3)$

That is,

Each point or vertex of the figure $\text{ABC}$ is to be moved $\text{4}$ units to the right along x-axis and $3$ units downalong y-axis to reach figure $\text{A'B'C'}$ .