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# Performing reflections: rectangle (old)

An older video where Sal uses the interactive widget to find the image of a rectangle under a reflection. Created by Sal Khan.

Video transcript

Perform a reflection
over the line y is equal to negative 1/3 x. And then they want
us to figure out what these different points
map to on the reflection. And then they ask, is the slope
of the segment between point A and its image is, and
then blank, the slope of the segment between
point B and its image. So let's just think
about this step by step. So first, let's perform the
reflection over the line y is equal to negative 1/3 x. So we want to reflect. So negative 1/3 x. So its y-intercept is 0. And it has a slope
of negative 1/3, which means every time-- whoops,
so let me put this right over here-- and that means every
time we move positive 3 in the x direction, we move
down once in the y direction. So this right over here, this
is y is equal to negative 1/3 x. And so let's do our reflection. Whoops. To do the reflection,
I've got to press this. So let's do our reflection. There we go. All right, this is exciting. So what does point A map to? Well, point A maps to this
point right over there. And so that is the
point negative 4, 8. And point B maps to this
point, which is the point 8, positive 4. And then, they say the slope
of the segment between point A and its image, so
that's this segment between point A and its image. So actually let me take this
reflection tool to just show you that line. So that's this segment
right over here. The slope of the segment
between point A and its image, that's this slope
right over here, is blank the slope
of the segment between point B and its image. Well, point B and its image,
that line right over here, is going to have the same slope. And that makes sense,
because they're both going to be perpendicular to
what we were reflecting around. They're both going to
be perpendicular to y is equal to negative 1/3 x. So they're going to have
a negative reciprocal of negative 1/3 slope,
which is positive 3. And you see this has
a slope of positive 3, and that this right over here
has a slope of positive 3. Every time you increase
one in the x direction, you increase y by three units. So the slope is equal to. And we check our answer. And we got it right.