Question

Find the image of O (0, 0) after two reflections, first in y = 4, and then in x = –7.

Answer 1

These are the answer options

(–14, 8)

(8, –14)

(7, –4)

(–4, 7)

Answer 2

y = 4 is the equation of a horizontal line at y = 4

The distance between (0, 0) and (y = 4) , is 4 units in the "y" direction.

The first reflection of (0, 0) about (y = 4) then is 4 units above (0, 4)
resulting in the point Rı = (0, 8)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

The second reflection is about the vertical line (x = - 7)

The distance between (0, 8) and (x = - 7) , is 7 units in the "- x" direction.

 ... so the reflection of (0, 8) about (x = - 7) then is 7 units to the left of (- 7, 8)
  resulting in the point Rıı = (-14, 8)

   Answer: (-14, 8)