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This video is provided as supplementary material
for courses taught at Howard Community College, and in this video
I'm going to demonstrate how to translate, or slide, an image
on a grid. So I'm go to translate
this orange quadrilateral. I've labeled it ABCD,
and I'm going to slide, or translate, it to times:
Once using this blues slide arrow, or vector,
and one more time using this red slide arrow,
or vector. Now what the vectors tell us
is two important pieces of information. They tell us how
far we're going to move the image. This vector, the blue one,
is four units long. So that tells us to move this image
four units. The direction that the vector is pointing,
tells me what direction I'm going to move the image in.
So let's take this blue vector
and translate image ABCD.
It's telling me I move the image four units
horizontally to the right. So I'll do this
one angle, one point at a time.
I'll start with point A, and I'm going to count from point A
four units over and
that's going to be the translation of point A. I'll call that place
A-prime. I'll do the same thing for the other three corners.
I'll take point B, count four units
and I'll label that as B-prime.
I'll count four units from C --
that's going to become
C-prime, And four units over to the right of D
will become D-prime. And now the only thing left to do
is connect those four points
and that will get me
my translated image.
Notice that the translated image is
exactly the same size as the original. It's just moved to a different location.
It hasn't rotated all any.
The angles are all congruent and the side are congruent.
It's exactly the same image, but it's in a different place.
Now let's take a look at the other vector. This red vector
goes at an angle, and that might be hard to work with.
So what we can do is we can break it down into two component parts.
From one end of the vector to the other, or from the beginning of the vector
to the end, we did two things:
we go up three units. I'm gonna think of that
direction, up three units, as one vector. And then we go over two units.
So I'll think of that as the second vector. And that gets me to
the end point of the original red vector. So I'm going to use that information
to translate this
orange quadrilateral again.
So I'll start at point A, go up three units
and then over two to the right. And I'll label that point
A-double prime. The same thing for point B.
I'll go up three units and over two to the right.
And that's now point
B-double prime. For point C, I go
three and two more to right. I'll label that.
And now for D.
Up three and two to the right. And that's
D-double prime. And I just have to connect those four points.
Once again,
I've got an image
thats exactly the same shape and size
as my original image. In other words, it's congruent with it.
And its orientation is the same: it hasn't rotated it all.
Okay, I hope that helps.
Take care, I'll see you next time.