ANSWER
The coordinates of the image are (2,2)
EXPLANATION
The mapping for a reflection across the line y=k is :
[tex](x,y)\to (x,2k-y)[/tex]
We want to find the image of the point (2,-4) after a reflection in the line y=-1.
In this case k=-1.
[tex](2, - 4)\to (2,2( - 1)- - 4)[/tex]
This simplifies to,
[tex](2, - 4)\to (2, - 2 + 4)[/tex]
[tex](2, - 4)\to (2, 2)[/tex]
Hence the image is (2,2)
