a>p=a'(-3,-3) for the glide reflection where the translation is (x,y)>(x+5,y) and the line of reflection is y=1. What are the coordinates of a'?

(x,y) -> (x+5,y) -> (x+5,1-(y-1)) = (x+5,2-y)

So, plug in your numbers

so would it be 2,-3 or 2,5

To find the coordinates of a' in the glide reflection, we can apply both the translation and the reflection to point a.

First, let's apply the translation. Given that the translation is (x, y) → (x + 5, y), we can find the new coordinates of a by adding 5 to the x-coordinate:

a' = (a + 5, b)

Next, let's apply the reflection over the line y = 1. To reflect a point over a line, we need to find the perpendicular distance between the point and the line, and then move the point in the opposite direction by that distance.

The perpendicular distance between a point (x, y) and the line y = 1 is the difference between the y-coordinate of the point and the y-coordinate of the line. In this case, it is:

d = y - 1

To reflect the point over the line, we need to move the point downwards by twice the perpendicular distance:

a'' = (a' + 0, b' - 2d)

In our case, since the line of reflection is y = 1, we have d = y - 1. Substituting the previously found expression for a' and d, we get:

a'' = (a + 5, b - 2(y - 1))

Now, let's substitute the given coordinates of a to find the final coordinates of a':

a'' = (-3 + 5, -3 - 2((-3) - 1))
= (2, -3 - 2(-4))
= (2, -3 + 8)
= (2 ,5)

Therefore, the coordinates of a' in the glide reflection are (2,5).