Question

Find the image of O (-2,-1) after two reflections, first across the line y=-5, and then across the line x=1.

I believe the answer should be (-1,-6)

Can someone please confirm?

Answer 1

Nope.

Reflecting across the line y = -5 means that the image is as far below the line as (-2,-1) is above it: 4 units. So,

(-2,-1) -> (-2,-9)

Same with the line x=1. 3 to the left, so 3 to the right.

(-2,-9) -> (4,-9)

Reflecting across the line y=k:

(x,y) -> (x,k-(y-k))

Across the line x-h:

(x,y) -> (h-(x-h),y)

So, the two reflections take

(x,y) -> (h-(x-h),k-(y-k))

In this case,

(-2,-1) -> (1-(-2-1),-5-(-1+5)) = (4,-9)