14. If you complete a glide reflection to the point H(-2, -3) with the translation (x, y) → (x – 2, y) and a reflection over y = -4. Find the point H”.

Question

Hint: Graph the point, complete the translation & then flip over the horizontal line.
*
(-4, -7)
(-2, -5)
(0, -5)
(-4, -5)

Answer 1

To start, let's apply the translation (x, y) → (x – 2, y) to point H(-2, -3):

H' = (x – 2, y) = (-2 – 2, -3) = (-4, -3)

Now, let's reflect point H' over y = -4. The distance of H' to the line y = -4 is 1 unit, so the reflected point H" will also be 1 unit away from the line on the other side.

Reflecting point H'(-4, -3) over y = -4:

H" = (-4, -3) → (-4, -3 - 2(1)) = (-4, -5)

Therefore, the point H" after completing the glide reflection is (-4, -5).