Chapter 11.4, Problem 7IP

To determine

To graph figure and its image after a reflection over the x -axis.

Explanation of Solution

Given:

Figure $ABCD$ where $A(-3,-1)$ , $B(-5,-1)$ , $C(-5,-6)$ , and $D(-3,-3)$ .

Graph of the original figure:

Use the given coordinates of the vertices of figure $ABCD$ to plot the graph.

  

Interpretation:

The figure $ABCD$ lies in the III quadrant. It represents a trapezoid.

Graph of the image after a reflection over the $x-\text{axis:}$

The coordinates after a reflection over $x-\text{axis}$ changes.

The $x$ coordinate remains the same but the sign of $y$ coordinate changes to the opposite.

  $(x,y)\to (x,-y)$

Let $A\text{'}B\text{'}C\text{'}D\text{'}$ be the image of figure $ABCD$ after a reflection over the $x-\text{axis}\text{.}$

So, the coordinates of the vertices of $A\text{'}B\text{'}C\text{'}D\text{'}$ are:

  $A\text{'}(-3,1)$

  $B\text{'}(-5,1)$

  $C\text{'}(-5,-6)$

  $D\text{'}(-3,3)$

Now by using the coordinates of vertices of $A\text{'}B\text{'}C\text{'}D\text{'}$ plot the graph.

  

Interpretation:

The figure $A\text{'}B\text{'}C\text{'}D\text{'}$ lies in the II quadrant.