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)
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)
To find the coordinates of P, we need to apply the transformations of glide reflection to the given point P'(-8, -3).
First, let's apply the translation by (x,y) -> (x, y-5) to P'(-8, -3):
P1 = P'(-8, -3) + (0, -5) = (-8, -8)
Next, let's apply the line reflection x = -5 to P1(-8, -8). Since x = -5 is a vertical line, the x-coordinate will stay the same, but the y-coordinate will change sign:
P2 = (-8, -8) reflected over x = -5 = (-2, -8)
Therefore, the coordinates of P are (-2, -8).
So, none of the options provided, (-8,-8), (-8,2), (-2,-3), (-2,2), are correct. The correct answer is (-2, -8).