Chapter 14.3, Problem 18WE

To determine

To construct:Glide reflection line that maps $\Delta ABC$ to $\Delta A\text{'}B\text{'}C\text{'}$ .

Answer to Problem 18WE

Glide reflection line constructed that maps $\Delta ABC$ to $\Delta A\text{'}B\text{'}C\text{'}$ using the midpoints of segments $\overline{AA\text{'}},\overline{BB\text{'}},\overline{CC\text{'}}$ .

Explanation of Solution

Given information :

$\Delta ABC$ to $\Delta A\text{'}B\text{'}C\text{'}$ are shown.

Concept used:

In 2-dimensional geometry, a glide reflection is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operation.

A translation moves ("slides") an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it.The original object is called the pre-image, and the translation is called the image.

As per the previous problem, the midpoints of segments $\overline{AA\text{'}},\overline{BB\text{'}},\overline{CC\text{'}}$ lie on the reflecting line.

Below diagram is provided in problem.

To get reflection line get midpoints of $\overline{AA\text{'}},\overline{BB\text{'}},\overline{CC\text{'}}$ , we will join $A$ to $A\text{'}$ , $B$ to $B\text{'}$ & $C$ to $C\text{'}$ .

Once we got the midpoints, we join the mid-points of $\overline{AA\text{'}},\overline{BB\text{'}},\overline{CC\text{'}}$ & thus we get the reflecting line.

Hence,

Glide reflection line constructed that maps $\Delta ABC$ to $\Delta A\text{'}B\text{'}C\text{'}$ using the midpoints of segments $\overline{AA\text{'}},\overline{BB\text{'}},\overline{CC\text{'}}$ .