Question

List the coordinates coordinates of vertices of trapezoid ABCD after it has been rotated 90 Counterclockwise bout the origin and then reflected over the x-axis. A(-5,-3) B(-4,0),c(-2,0),D(O,-3)

Answer 1

The coordinates of the final image is;

`A^(\prime\prime)(3,5),B^(\prime\prime)(0,4),C^(\prime)^(\prime)(0,2),D^(\prime)^(\prime)(3,0)`

Step-by-step explanation:

From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.

Which has a rule;

`(x,y)\rightarrow(-y,x)`

Applying the rule to the given points. we have;

`\begin{gathered} A(-5,-3)\rightarrow A^(\prime)(3,-5) \\ B(-4,0)\rightarrow B^(\prime)(0,-4) \\ C(-2,0)\rightarrow C^(\prime)(0,-2) \\ D(0,-3)\rightarrow D^(\prime)(3,0) \end{gathered}`

Then the produced image was then reflected over the x-axis;

Reflection across the x-axis have the rule;

`(x,y)\rightarrow(x,-y)`

Applying the rule to the resulting image;

`\begin{gathered} A^(\prime)(3,-5)\rightarrow A^{\prime^{}}^(\prime)(3,5) \\ B^(\prime)(0,-4)\rightarrow B^(\prime)^(\prime)(0,4) \\ C^(\prime)(0,-2)\rightarrow C^{\prime^{}}^(\prime)(0,2) \\ D^(\prime)(3,0)\rightarrow D^(\prime)^(\prime)(3,0) \end{gathered}`

Therefore, the coordinates of the final image is;

`A^(\prime\prime)(3,5),B^(\prime\prime)(0,4),C^(\prime)^(\prime)(0,2),D^(\prime)^(\prime)(3,0)`