Question

P -> P' (4, 2) by a glide reflection, consisting of a translation followed by a reflection. The translation is (x,y) -> (x,y + 3) and the line of

reflection is x = 0. What are the coordinates of P?

Answer 1

Since P is transformed to P' by a glide reflection consisting of a translation and a reflection, we can first apply the translation to P and then reflect the result about the line x=0 to get P'.

Let P = (x, y) be the coordinates of P. Then the translation of P is given by:

P1 = (x, y + 3)

To reflect P1 about the line x=0, we negate the x-coordinate of P1, giving:

P' = (-x, y + 3)

We know that P' has coordinates (4, 2), so we can set the x and y values equal to 4 and 2 respectively, and solve for x and y:

x = 4, so x = -4
y + 3 = 2, so y = -1

Therefore, the coordinates of P are (x, y) = (-4, -1)