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: