Chapter 12.4, Problem 3E

To determine

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

Answer to Problem 3E

Each point or vertex of the figure $\text{ABC}$ is to be moved $3$ units to the leftalong x-axis and $\text{4}$ 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 of triangle $\text{ABC}$ to $\text{A'B'C'}$ :

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

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

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

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

  $(x,y)\to (x-3,y-4)$

That is,

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