Question

GIVING MEDAL.
The figure is reflected across line m and then reflected across line n. What is the resulting transformation?
A. glide reflection
B. translation
C. reflection
D. rotation

Answer 1

Let's go through the possibilities. Do you know what a glide reflection is?

Answer 2

i know what it looks like, dunno how to explain it tho.

Answer 3

Okay, is this one of them? :-)

Answer 4

A glide slope involves both a reflection across a line and a translation along that line.

Answer 5

i don't think so..

Answer 6

oh

Answer 7

Good. It's not, because the shape isn't going to move parallel to those lines.

Answer 8

How about rotation, is that going to happen here?

Answer 9

i don't think it's rotation either

Answer 10

i think that it's a translation, but im not sure.

Answer 11

Think about smearing something sticky on a piece of paper, then folding the paper over along the line labeled m. You'll get a copy of the figure on the other side of the line, right?

Answer 12

yes. so it's reflection?

Answer 13

If you unfold the paper, and then crease along the other line, you get another copy of the figure, right? It won't be in the same spot as the original, but it will be on the original's side of the second line...

Answer 14

ok

Answer 15

it should have the same orientation — the point on the top should point in exactly the same direction

Answer 16

ohh

Answer 17

so, same orientation, same shape, but moved to a different spot, what is that called?

Answer 18

i dunno :(

Answer 19

we ruled out glide reflection and rotation. that leaves reflection and translation. we've done two reflections, so that can't be it — we're looking for a single operation which accomplishes the effect of the two operations we've done. We have a symmetrical figure here, but if we had on that was not, two reflections couldn't be reproduced by one reflection, right?

Answer 20

yeah.

Answer 21

so that leaves us only one answer :-)

Answer 22

so it's translation

Answer 23

yes. it's a bit harder to see in this diagram because the line goes at a diagonal. Think of a reflection across the y-axis. That's going to flip a shape from the left side of the y-axis, to the right side of the y-axis. If we then do another reflection across a line parallel to the y-axis but much closer to the reflected shape, we'll end up with the shape being somewhere between the original shape and the first reflected shape, but in the same orientation, size, etc. In other words, a translation.

Answer 24

thank you so much. i really appreciate it.

Answer 25

you're welcome.