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This isn't to bad if you think about it and you kinda know what you're dealing with. Do reflecting, translating, or rotating the triangle change the size, shape, and [therefore] the perimeter in any way? That's kinda the point of this question.
so, to begin with, how would you calculate the perimeter of the triangle?
um, a+b+c= perimeter
yes... so before you do any of the operations in a, b, or c to the triangle, the perimeter that you calculate is the perimeter of the pre-image.
yeah, so what do I do then?
well, a, b, and c are each asking you to redraw the triangle. If I were doing the problem, I'd redraw them on separate graphs. 5a wants you to simply to draw the triangle rotated 180 degrees.
I know, but like I just can't seem to figure out how to rotate it, I can do the translation part, and maybe even the reflection part
It's tricky, cause it's not telling you how to do it - there are different ways to do it, but I'm assuming that the question is trusting that you have the spatial reasoning skills to redraw it... I'm also assuming they are suggesting a rotation about it's center.
In this case, it would be easiest to rotate it about the center of the hypoteneuse though... it would also make the numbers nicer to deal with. I'll draw you an example:
draw the example so i know what your talking about
thanks for helping btw :D
okay so the reflection would be like this (I'll draw it) right ?
yeah. Now what I drew was the rotation. The reflection on the y-axis looks a little different too:
this is from the rotated one
ah... I'm sorry, you right... it should be rotated about the orgin... not just rotated. which would be like this:
If you want to know how I rotated it. I drew a line between the origin and a point on the triangle, then I found the line 180 degrees in the different direction (which at 180 degrees happen to be the same line), then drew the point on that line at a distance equal to the distance on the original line. This works for any rotation about the origin for all the points. Then you just reconnect the triangle. (ie. Rotation at 90 degrees):
that's a 90 degree rotation about the orgin. If you did it for all three points, you could reconstruct the triangle (and that would be a 90 degree rotation). Confusingly... a 90 degree rotation is the exact same as a y-axis reflection in this situation.... however, I only wanted to illustrate how you could rotate (at different angles) around the origin.
wait so what would the end result be?
sorry I left for a while
The whole point of the exercise is to see that the pre-image and post-image perimeters of the triangle are the same after applying rotation, translation, or reflection transformations.
which ones have you exampled?
because my one was different than yours
180 degree rotation about the origin and reflection about the y-axis. If you follow what I wrote, which-is-which is clear enough.
... well thanks for helping I guess...