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”.
Hint: Graph the point, complete the translation & then flip over the horizontal line.
*
(-4, -7)
(-2, -5)
(0, -5)
(-4, -5)
The original point H is (-2, -3).
1. Applying the translation (x, y) → (x – 2, y) to H(-2, -3):
H' = H(-2-2, -3) = H(-4, -3)
2. Reflecting H' over the horizontal line y = -4:
H" = (-4, -4 - (-3 - (-4))) = (-4, -4 + 1) = (-4, -3)
Therefore, the point H" is (-4, -3).