Question

P->P'(-8,-3) for the glide reflection where the translation is (x,y)->(x,y-5) and the line reflection is x=-5. what are the coordinates of P?

(-8,-8)
(-8,2)
(-2,-3)
(-2,2)

Answer 1

well, just do what the rule says:

(x,y)->(x,y-5) = (-8,-3)
means
x = -8 and y-5 = -3
x = -8 and y = 2

reflection: (x,y)->(-5-(x+5),y) = (-x-10,y)
glide:
(x,y)->(x,y-5) means
(-x-10,y) -> (-x-10,y-5)

So,
P->(-8,-3) = (-x-10,y-5)
means that
-x-10 = -8
y-5 = -3

x = -2
y = 2

So, P(-2,2) -> (-8,-3)