Question

What are the coordinates of each point after quadrilateral ABCD is reflected across the y axis and then translated 2 units down?

Answer 1

First, let's write the vertices of the quadrilateral ABCD.

According to the given image, the vertices are A(1,1), B(2,3), C(4,3), D(5,1).

The first transformation a reflection across the y-axis means we have to multiply each x-coordinate by -1 to change its sign.

`\begin{gathered} A(1,1)\rightarrow A^(\prime)(-1,1) \\ B(2,3)\rightarrow B^(\prime)(-2,3) \\ C(4,3)\rightarrow C^(\prime)(-4,3) \\ D(5,1)\rightarrow D^(\prime)(-5,1) \end{gathered}`

The second transformation a translation 2 units down means we have to subtract 2 units from each y-coordinate.

`\begin{gathered} A^(\prime)(-1,1)\rightarrow A^(\doubleprime)(-1,1-2)\rightarrow A^(\doubleprime)(-1,-1) \\ B^(\prime)(-2,3)\rightarrow B^(\doubleprime)(-2,3-2)\rightarrow B^(\doubleprime)(-2,1) \\ C^(\prime)(-4,3)\rightarrow C^(\doubleprime)(-4,3-2)\rightarrow C^(\doubleprime)(-4,1) \\ D^(\prime)(-5,1)\rightarrow D^(\doubleprime)(-5,1-2)\rightarrow D^(\doubleprime)(-5,-1) \end{gathered}`

Once we made both transformations, we can draw the quadrilateral.

Therefore, the new vertices are (-1,-1), (-2,1), (-4,1), and (-5, -1).