Question

P → P' (2, –6) for the glide reflection where the translation is (x, y) → (x + 2, y –2) and the line of reflection is y = – x. Find the coordinates of P.

Answer 1

To find the original coordinates of point P before a glide reflection, we reverse the translation of P' (2, -6) by subtracting 2 from the x-coordinate and adding 2 to the y-coordinate, resulting in P (0, -4).

Step-by-step explanation:

The student is asking for the original coordinates of a point P before it undergoes a glide reflection. The glide reflection consists of a translation followed by a reflection over the line y = -x. The translation moves any point (x, y) to (x + 2, y - 2). Given that after this transformation, point P has coordinates P' (2, -6), we need to reverse the translation to find the original coordinates of P. We subtract 2 from the x-coordinate and add 2 to the y-coordinate of P', giving us the coordinates of P as (0, -4). Now P can be reflected over the line y = -x to get P'.