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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 show how to reflect an image on a grid. So
the image I'm going to use is this quadrilateral.
I've labeled it ABCD and I'm going to reflect it across this
blue line. We'll call that line 'l'. So what I want to do is start at point A
and find the distance from point A
to line 'l' -- that's one unit --
and then go one unit further the same direction. And I'll label that
as point A-prime. I'll do the same thing for point B.
Point B is four units
from line 'l'. I'll go four units further
and that will get me to B-prime.
Notice, by the way, that if I connected a line between B and
B-prime, that line would be perpendicular
to line 'l'. The same thing would happen if I connected point A
and A-prime. I'd have a line perpendicular line 'l'.
I'll go to point C. Point C is
three units from line 'l'. That's going to be point C-prime.
and it's going to be C-prime. And point D
is five units from line 'l'.
So I'll continue in the same direction. I'll go five units further
and that gets me to D-prime.
Now I'll take a straight edge and connect points
A-prime and B-prime, B-prime and C-prime,
C-prime to D-prime,
and D-prime to A-prime.
And there
I've got my original image, ABCD,
reflected across line 'l'
to create its mirror image, A-prime B-prime C-prime D-prime.
When you're working with reflections
cross a horizontal or vertical line,
that's fairly easy. What's a little bit harder is doing a reflection across
a diagonal line,
a 45-degree diagonal. So I'm going to draw a new line.
I'll put this at a 45 degree angle,
like this and we'll reflect that image one more time,
this time using this line. I'll label that as line 'm'.
Okay, so
I'll start at point A,
and point A is 1 1/2
units diagonally from line m.
So I want to go diagonal again, at a 45 degree angle,
further in that direction. I'll go diagonally 1 1/2 units
and that will take me to a point I'll label A-double prime.
Point B is
1/2 unit diagonally from line m,
so I'll go 1/2 unit more and that will take me to B-double prime.
Once again, if i connected, let's say, point A-double prime and point A,
I would have a line that went perpendicular
to line m. The same thing would happen with points
B and B-double prime. Let's go on to point C.
I have to go one unit diagonally to line m.
So I'll go one more unit. That will get me to C -double prime.
And point D is
three units diagonally away. So I'll go three units more.
That would get me to D-double prime.
Okay, now let's connect these points. So let's see... I've got
A-double prime and B-double prime,
There we go.
And then B-double prime to C-double prime.
It's always a good idea, especially with a complicated image,
to label your points,
because otherwise it's fairly easy to get confused
I connect the wrong points.
and there's D-double prime to A-double prime.
Now this is my reflected image.
It looks a little bit confusing this way. If I turn this
paper at a 45-degree angle,
I think it's a lot easier to see that what I've got is a mirror image
reflected across line m. This should look
symmetrical. Okay, that's about it.
Take care, I'll see you next time.