Chapter 11, Problem 16CR

To determine

To find: The vertices after a reflection over the x-axis.

Answer to Problem 16CR

Vertices of Figure after reflection are

  $\begin{array}{l}A\text{'}\left(1,3\right)\\ B\text{'}\left(4,3\right)\\ C\text{'}\left(1,1\right)\\ D\text{'}\left(-2,1\right)\end{array}$

Explanation of Solution

Given information:

Vertices of figure $ABCD$ are

  $\begin{array}{l}A\left(1,-3\right)\\ B\left(4,-3\right)\\ C\left(1,-1\right)\\ D\left(-2,-1\right)\end{array}$

For reflection over x-axis

We need to Use same x-coordinate and replace y-coordinate with its opposite.

Given

Vertices of figure $ABCD$ are

  $\begin{array}{l}A\left(1,-3\right)\\ B\left(4,-3\right)\\ C\left(1,-1\right)\\ D\left(-2,-1\right)\end{array}$

On reflection over x-axis

We get

  $\begin{array}{l}A\left(1,-3\right)\to A\text{'}\left(1,-\left(-3\right)\right)\\ \Rightarrow A\left(1,-3\right)\to A\text{'}\left(1,3\right)\\ B\left(4,-3\right)\to B\text{'}\left(4,-\left(-3\right)\right)\\ \Rightarrow B\left(4,-3\right)\to B\text{'}\left(4,3\right)\\ C\left(1,-1\right)\to C\text{'}\left(1,-\left(-1\right)\right)\\ \Rightarrow C\left(1,-1\right)\to C\text{'}\left(1,1\right)\\ D\left(-2,-1\right)\to D\text{'}\left(-2,-\left(-1\right)\right)\\ \Rightarrow D\left(-2,-1\right)\to D\text{'}\left(-2,1\right)\end{array}$

Therefore,

Vertices of Figure after reflection are

  $\begin{array}{l}A\text{'}\left(1,3\right)\\ B\text{'}\left(4,3\right)\\ C\text{'}\left(1,1\right)\\ D\text{'}\left(-2,1\right)\end{array}$