Question

Help, it's for my exam tomorrow! I don't understand this./:
Perform a glide reflection on point (2, -5) that is translated by (x, y) (x - 4, y + 1) and then reflected over the x-axis. What are the coordinates of the image point?

Answer 1

I would break it into two steps:
1.) Perform translation of (x, y) --> (x - 4, y + 1)
2.) Reflect over x-axis.


1.) We know (x, y) = (2, -5) (The given point). More specifically, x=2 and y=-5.
To perform this shift, we simply plug in our new values of x and y for our shift parameters:
(x - 4, y + 1) <-- (x, y) = (2, -5)
(2 - 4, -5 + 1)
In words, we took the x-value and moved it back 4 units, and then took the y-value to move it up one unit. We simplify then.

2.) To reflect over the x-axis, we are essentially taking the same point with the opposite value of y. This means that we are in a sense transforming the point we obtained from above like this: (x, y) --> (x, -y). Visually, this is what we were looking to do.

So, our new (x, y) is what we obtained from the last transformation. Then we simply substitute the x and y-values to get our final answer.


Summarized Method: (x, y) --> (x - 4, y + 1) = (x2, y2); (x2, y2) --> (x2, -y2) will be our final point position.