Answer:
Reflecting over the line x = -5 then reflecting over the line y = 4 is the same as a horizontal translation to, 2 times the x-coordinate value and then moving 10 units to right and a vertical translation of two times the y-coordinate value and then moving 8 units down, given as follows;
Coordinates of the preimage is (x, y)
Coordinate of the image will become ((2·x + 10), (2·y - 8))
Explanation:
Reflecting over the line x = -5 gives the x-coordinate of the image as being equidistant from the line x = -5 as the preimage while the y-coordinate remain unchanged
Therefore, we have;
Coordinates of the preimage = (x, y)
Coordinates of the image = (2×(x - (-5)), y) = (2×(x + 5), y)
Similarly, for the reflection across the line y = 4, the x-coordinate value remain unchanged and therefore. we have;
Coordinates of the preimage = (x, y)
Coordinates of the image = (x, 2×(y - 4))
The cumulative transformation becomes
Coordinates of the preimage = (x, y)
Coordinates of the image = (2×(x + 5), 2×(y - 4)) = ((2·x + 10), (2·y - 8))
Which is the same as a horizontal translation to, twice the x-coordinate value and then moving 10 units to right and a vertical translation of twice the y-coordinate value and then moving 8 units down.