Chapter 11.4, Problem 6IP

To determine

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

Explanation of Solution

Given:

Figure $RSTV$ where $R(2,4)$ , $S(4,3)$ , $T(4,-2)$ , and $V(1,-2)$ .

Graph of the original figure:

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

  

Interpretation:

The figure $RSTV$ lies in the I and IV quadrants. It represents an irregular polygon.

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

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

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

  $(x,y)\to (-x,y)$

Let $R\text{'}S\text{'}T\text{'}V\text{'}$ be the image of figure $RSTV$ after a reflection over the $y-\text{axis}.$

So, the coordinates of the vertices of $R\text{'}S\text{'}T\text{'}V\text{'}$ are:

  $A\text{'}(-2,4)$

  $B\text{'}(-4,3)$

  $C\text{'}(-4,2)$

  $D\text{'}(-1-2)$

Now by using the coordinates of vertices of $R\text{'}S\text{'}T\text{'}V\text{'}$ plot he graph.

  

Interpretation:

The figure $R\text{'}S\text{'}T\text{'}V\text{'}$ lies in the II and IV quadrants.