Chapter 9.4, Problem 42HP

To determine

To find: The glide reflection or the composition of the transformation such that it can be use to transform triangle ABC to DEF.

Answer to Problem 42HP

The $\Delta ABC$ is translated along $\left(0,-4\right)$ and reflected in $x=-1$ to form $\Delta DEF$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure

Calculation:

Consider the given triangles ABC and DEF it is shown that BC and EF have the same slope as the angle A and D are right angles. Thus, the point A to D and point B to E and Point C to F.

The x coordinate of the point C and F are two units’ parts and the y coordinate of B and E are 4 units apart. The first step is to translate ABC along the vector $\left(0,-4\right)$ such that each pair of corresponding points is on the same horizontal lie. The next step is to reflect triangle ABC in the line $x=-1$ to transform as $\Delta ABC$ to DEF.

Thus, $\Delta ABC$ is translated along $\left(0,-4\right)$ and reflected in $x=-1$ to form $\Delta DEF$ .