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### Course: Geometry (all content) > Unit 10

Lesson 9: Old transformations videos# 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.

## Want to join the conversation?

- So the slope of a line never changes if it is reflected across a line of the same slope?(22 votes)
- But if it is reflected across a line that has a slope of 0 or opposite. Then the slope may change to being a positive or negative.(1 vote)

- Does programming involve some math?(5 votes)
- Everything in the real world includes math including the room you are sitting in now(1 vote)

- Can't we move the whole line instead of moving the points to find out if the slope is the same between the point and it's image?(4 votes)
- You can, it is just easier for some people to understand moving the points instead of moving the whole line. However, I do prefer moving the line and if you find it easier, I wholly recommend doing it how you feel comfortable.(4 votes)

- Why is the y intercept at zero? just wondering.(3 votes)
- Can a reflection always be used in place of a rotation and translation?

I noticed while working the problems that I could usually come up with a reflection (one step that solved the problem instead of using a rotation and translation (two steps) and I am wondering if that is generally true?(3 votes)- yah i agree on your saying i think that reflection always is used in place of a rotation.(1 vote)

- What does the equation mean? How do you use it to find the slope for the reflection?(2 votes)
- My question is, how am I suppose to perform reflections on pieces of paper, without the reflect tool that Khan Academy provides? Really confused, test coming up, help!(2 votes)
- you count from the x/y axis line to your position/dot. then, you go to the the other side of the x/y axis and count the same number of spaces towards the opposite direction.

hope you ace your test!(2 votes)

- What does it mean to say a figure has rotational symmetry?(2 votes)
- If an object has rotational symmetry, it means that if you rotate a part of it around, it will look the same as another part of the same object. Hmm, it's kinda hard to explain. Maybe this will help:

https://upload.wikimedia.org/wikipedia/commons/thumb/3/36/The_armoured_triskelion_on_the_flag_of_the_Isle_of_Man.svg/330px-The_armoured_triskelion_on_the_flag_of_the_Isle_of_Man.svg.png

So, the figure pasted above has rotational symmetry because if you rotate one 'leg' around far enough, it will be the exact same shape as another leg in the same image. Make sense?(1 vote)

- what is the reflection of triangle (1,4) (3,-2) (4,2) over the x-axis?(1 vote)
- Fractions in coordinate plane? I am Confused. 1/3x ?(2 votes)
- You may already know after 12 days but to be clear, a linear slope is always the (change in y) over (change in x)

(y2-y1) / (x2-x1) where y2 and x2 is a coordinate (x2, y2) at any two points and y1 and x1 are different coordinates at any two points (x1,y2)

(the 1 and 2 should be smaller numbers)

this will give you the slope.

The slope represent that any number that slope mulitplies with x will be y in a y=slope * x

(usually the linear equations looks like y = kx + b where k is slope)

for y = slope * x, the slope is -1/3 x, so if x = 3 then y = (-1*3)/3 = -1

gives coordinate (3,-1)

if x is = 9, then y = (-1*9)/3 = -3

gives coordinate (9, -3)

and

you can see this is true when change in y/change in x = slope

(-3-(-1))/(9-(3)) = (-2/6) = -1/3

hope this made sense or helped.(0 votes)

## 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.