Question

how do you perform a glide reflection by translating ABC left 10, down 11, then reflect across the x-axis. also give coordinates for the first image A' B' C' and A'' B'' C''the pre-image is A(3,11) B(3,4) C(10,4)

Answer 1

A glide reflection consists firs of a translation (either horizontal, or vertical or both) and then a reflection across some line.

In our case we are given the pre-image coordinates:

A = (3, 11)

B = (3, 4)

C = (10, 4)

So for the translation 10 units left and 11 units down, we need to subtract from the x-coordinates 10 (left 10 units), and subtract for the y-coordinate 11 (down 11 units). Then A', B', and C' become:

A' = (-7, 0)

B' = (-7, -7)

C' = (0, -7)

Now we need to reflect these points across the x-axis. So, recall that such a reflection keeps the x-coordinate intact, and changes the y-coordinate to its opposite value. Then the new coordinates become:

A" = (-7, 0)

B" = (-7, 7)

C" = (0, 7)