Question

reflect triangle ABC over the line Y equals to translate the image right three and up to. Then what are the coordinates of the verticals in the image

Answer 1

`\begin{gathered} A^(\prime)^(\prime)(-2,4) \\ B^(\prime)^(\prime)(-3,7) \\ C^(\prime)^(\prime)(0,6) \end{gathered}`

Step-by-step explanation

First, let us find the coordinates of the vertices of the triangle:

`\begin{gathered} A(-5,2) \\ B(-6,-1) \\ C(-3,0) \end{gathered}`

Now, we have to reflect the points over the line y = 2.

To do this, find the distance between the y-coordinate of each vertex and y = 2 and add it to 2. That becomes the new y-coordinate of the point while its x-coordinate remains the same.

Therefore, the coordinates become:

`\begin{gathered} A(-5,2)\rightarrow A^(\prime)(-5,(2-2)+2)\Rightarrow A^(\prime)(-5,2) \\ B(-6,-1)\rightarrow B^(\prime)(-6,(2-(-1)+2)\Rightarrow B^(\prime)(-6,5) \\ C(-3,0)\rightarrow C^(\prime)(-3,(2-0)+2)\Rightarrow C^(\prime)(-3,4) \end{gathered}`

Now, we have to translate the points 3 units right and 2 units up. To do that, add 3 units to the x-coordinates and add 2 units to the y-coordinates of A'B'C':

`\begin{gathered} A^(\prime)(-5,2)\rightarrow A^(\prime)^(\prime)(-5+3,2+2)\rightarrow A^(\prime)^(\prime)(-2,4) \\ B^(\prime)(-6,5)\rightarrow B^(\prime)^(\prime)(-6+3,5+2)\rightarrow B^(\prime)^(\prime)(-3,7) \\ C^(\prime)(-3,4)\rightarrow C^(\prime)^(\prime)(-3+3,4+2)\rightarrow C^(\prime)^(\prime)(0,6) \end{gathered}`

That is the answer.