Chapter 14.3, Problem 10WE

To determine

To find:Glide reflection map $(x,y)$ .

Answer to Problem 10WE

The glide reflection is $(x,y)\to (x-7,-y)$ .

Explanation of Solution

Given information :

$\Delta A\text{'}B\text{'}C\text{'}$ is image under glide of $\Delta ABC$ move left 7 units and $\Delta A"B"C"$ is image under reflection of $\Delta A\text{'}B\text{'}C\text{'}$ in the $x-$ axis.

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 given problem

$\Delta A\text{'}B\text{'}C\text{'}$ is image under glide of $\Delta ABC$ move left 7 units and $\Delta A"B"C"$ is image under reflection of $\Delta A\text{'}B\text{'}C\text{'}$ in the $x-$ axis.

Since, $\Delta A\text{'}B\text{'}C\text{'}$ is image under glide of $\Delta ABC$ move left 7 units.

  $(x,y)\to (x-7,y)$

$\Delta A"B"C"$ is image under reflection of $\Delta A\text{'}B\text{'}C\text{'}$ in the $y-$ axis.

Here, substitute $y-$ coordinates with opposite (negative) numbers.

  $(x-7,y)\to (x-7,-y)$

Hence,

The glide reflection is $(x,y)\to (x-7,-y)$ .