So first of all we need to list the three points A, B and C so we can properly calculate the transformation:
[tex]\begin{gathered} A=(-3,3) \\ B=(-5,5) \\ C=(-4,6) \end{gathered}[/tex]
The first transformation we have to perform is a 90° clockwise rotation about the origin. If we perform this rotation on a point (x,y) we get:
[tex](x,y)\rightarrow(y,-x)[/tex]
Then we apply this to A, B and C:
[tex]\begin{gathered} A=(-3,3)\rightarrow A^{\prime}=(3,3) \\ B=(-5,5)\rightarrow B^{\prime}=(5,5) \\ C=(-4,6)\rightarrow C^{\prime}=(6,4) \end{gathered}[/tex]
Then we must perform a reflection over the x-axis on the points of triangle A'B'C'. A reflection over the x-axis is achieved by applying this transformation:
[tex](x,y)\rightarrow(x,-y)[/tex]
If we transform points A', B' and C' with this we get:
[tex]\begin{gathered} A^{\prime}=(3,3)\rightarrow A^{\prime}^{\prime}=(3,-3) \\ B^{\prime}=(5,5)\rightarrow B^{\prime\prime}=(5,-5) \\ C^{\prime}=(6,4)\rightarrow C^{\prime\prime}=(6,-4) \end{gathered}[/tex]
Then if we graph all the three triangles in the same grid we get the following picture:
As you can see this image is the same as the one in option D. This means that the answer to this question is graph D.
