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## High school geometry (staging)

### Course: High school geometry (staging) > Unit 1

Lesson 5: Reflections# Reflecting shapes

Let's reflect a quadrilateral across the x-axis. To do this, we find new points (A', B', C', D') by keeping the same x-coordinates and changing the y-coordinates to their opposite signs. This creates a flipped image of the original quadrilateral.

## Want to join the conversation?

- this is still complicated to me(19 votes)
- I suggest also looking at Algebra I concepts on transformations before coming to the High School Geometry section.(2 votes)

- So. Say you don't have a graph. How would you find out the coordinates with out using a graph to find the refection.(6 votes)
- You can use a formula. When you reflect over x-axis the coordinates are (x,-y) and when you reflect over the y-axis the coordinates are (-x,y. If you want to reflect over y=x then the coordinates are (y,x) If you want to reflect over y=-x the coordinates are (-y,-x)(18 votes)

- What is the X axis?(0 votes)
- the x axis is the principal or horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates.(10 votes)

- ah yes, triangle abcd(5 votes)
- ah yes, abcd, the easiest letters to use as variables aside from x, y and z(2 votes)

- 2:30it looks like a rotation not a reflection how is it a reflection(3 votes)
- Because as Sal showed it in the video, all the points are at the same distance from the other point. Like for point A, it is 4 above the x-axis, so he put A' (A prime) -4 from the x-axis. Does that help?(3 votes)

- was anyone else assigned 58 khan academy assignments by their math teacher or was it just me to suffer ?(4 votes)
- this still troubles me because on the khan assignment that i am working on it does not have an x or y axis or any numbers just line "l"(3 votes)
- The "l" line is just a reflection line.

Look at the line as if it's a mirror.

Say you want to reflect the letter A on this illustration:

-A--|----

Notice that A is 3 units away from the line.

So a reflection would look like this:

-A--|--A-

It's exactly like reflecting over Y, except we don't specify that the line is Y. It's just a reflection line.(1 vote)

- When do you know when the shapes size changes(3 votes)
- The reflections don't change the size of the shape instead only reflect. I think you are thinking about dilations.(1 vote)

- on way here is question from 5-6 years ago.(2 votes)

## Video transcript

- [Instructor] We're
asked to plot the image of quadrilateral ABCD so that's this blue quadrilateral here. Under a reflection across the X axis. So that's the X axis. And we have our little
tool here on Khan Academy where we can construct a quadrilateral. And we need to construct a reflection of triangle A, B, C, D. And so what we can do
is, let me scroll down a little bit. So we can see the entire coordinate axis. We want to find the
reflection across the X axis. So I'm gonna reflect point by point. And actually, let me just
move this whole thing down here so that we can so that we can see what is going on a little bit clearer. So let's just first reflect point let me move this a little
bit out of the way. So let's first reflect Point A. So we're gonna reflect across the X axis. A is four units above the X axis. One, two, three, four. So, its image, A prime we could say, would be four units below the X axis. So, one, two, three, four. So let's make this right over here A, A prime. I'm having trouble putting the let's see if I move these other characters around. Okay, there you go. So this is gonna be my A prime. Now let me try B. B is two units above the X axis. So B prime is gonna have
the same X coordinate but it's gonna be two
units below the X axis. So let's make this our B. So this is our B right over here. Now let's make this our C. C, right here, has the X coordinate of negative five. A d a Y coordinate of negative four. Now C prime would have
the same X coordinate but instead of being four
units below the X axis, it will be four units above the X axis. So it would have the
coordinates negative five comma positive four. So this is going to be our C here. So this goes to negative five, one, two, three, positive four. And then last but not least, D. And so let's see, D right now is at negative two comma negative one. If we reflect across the X axis instead of being one
unit below the X axis, we'll be one unit above the X axis. And we'll keep our X
coordinate of negative two. And so, there you have it. We have constructed the reflection of ABCD across the X axis. And what's interesting about this example is that, the original quadrilateral is on top of the X axis. So you an kind of see this top part of the quadrilateral
gets reflected below it. And this bottom part of the quadrilateral gets reflected above it. And then you can see that indeed do they indeed do look like reflections flipped over the X axis.