Question

Complete the row showing the coordinates ofpoints A-E and their images after a reflection inthe x-axis, followed by a reflection in the y-axis.

Answer 1

The original figure is formed by the points:

$\begin{gathered} A(-5,1) \\ B(-2,5) \\ C(0,2) \\ D(-2,3) \\ E(-3,0) \end{gathered}$

To first make a reflection in the x-axis, we must follow the rule:

$P(x,y)\rightarrow P^{\prime}(x,-y)$

So, let's use this transformation with each point:

$\begin{gathered} A^(-5,1)\rightarrow A^{\prime}(-5,-1) \\ B(-2,5)\rightarrow B^{\prime}(-2,-5) \\ C(0,2)\rightarrow C^{\prime}(0,-2) \\ D(-2,3)\rightarrow D^{\prime}(-2,-3) \\ E(3,0)\rightarrow E^{\prime}(-3,0) \end{gathered}$

Finally, we're asked to transform these previous points using a reflection in the y-axis. To do this we must use the following rule:

$Q(x,y)\rightarrow Q^{\prime}(-x,y)$

So, using this rule for the points already reflected in the x-axis:

$\begin{gathered} A^{\prime}(-5,-1)\rightarrow A^{^{\prime}\prime}(5,-1) \\ B^{\prime}(-2,-5)\rightarrow B^{\prime}^{\prime}(2,-5) \\ C^{\prime}(0,-2)\rightarrow C^{\prime}^{\prime}(0,-2) \\ D^{\prime}(-2,-3)\rightarrow D^{\prime}^{\prime}(2,-3) \\ E^{\prime}(-3,0)\rightarrow E^{\prime\prime}(3,0) \end{gathered}$

Finally, plot these points: