Chapter 14.3, Problem 8WE

To determine

To graph: $\Delta ABC,\Delta A\text{'}B\text{'}C\text{'}\&\Delta A"B"C"$ .

Answer to Problem 8WE

The graph of $\Delta ABC,\Delta A\text{'}B\text{'}C\text{'}\&\Delta A"B"C"$ is drawn on graph.

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.

  $A(4,2),B(7,0)\&C(9,-3)$

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.

  $A(4,2),B(7,0)\&C(9,-3)$

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

  $\begin{array}{l}A(4,2)\to A\text{'}(4-7,2)=(-3,2)\\ B(7,0)\to B\text{'}(7-7,0)=(0,0)\\ C(9,-3)\to C\text{'}(9-7,-3)=(2,-3)\end{array}$

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

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

  $\begin{array}{l}A\text{'}(-3,2)\to A"(-3,-2)\\ B\text{'}(0,0)\to B"(0,0)\\ C\text{'}(2,-3)\to C"(2,3)\end{array}$

Hence,

The graph of $\Delta ABC,\Delta A\text{'}B\text{'}C\text{'}\&\Delta A"B"C"$ is drawn on graph.