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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.

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• 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)
• 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.