Question

What are the coordinates of the vertices of triangle C', M', and S'? The initial directions are in the pic below.

Answer 1

The reflection across the x-axis is made by changing the sign of the y coordinate and maintaining the x coordinate, that is:

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

So, we can just apply this transformation to each vertex of the original triangle:

`\begin{gathered} C=(-3,-4)\to C^(\prime)=(-3,-(-4))=(-3,4) \\ M=(-3,6)\to M^(\prime)=(-3,-6) \\ S=(-6,5)\to S^(\prime)=(-6,-5) \end{gathered}`

So, the coordinates of the image triangle are:

`\begin{gathered} C^(\prime)=(-3,4) \\ M^(\prime)=(-3,-6) \\ S^(\prime)=(-6,-5) \end{gathered}`