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## Geometry (all content)

### Unit 6: Lesson 4

Reflecting points on coordinate plane# Reflecting points in the coordinate plane

Just like looking at a mirror image of yourself, but flipped....a reflection point is the mirror point on the opposite side of the axis. Watch this tutorial and reflect :). Created by Sal Khan.

## Want to join the conversation?

- the x-axis and the y-axis is like a tool to help reflect(8 votes)
- How would you reflect a point over the line y=-x?(6 votes)
- It works just like any line, graph it and follow the line reflection rules. :)(3 votes)

- What happens if it tells you to plot 2,3 reflected over x=-1(4 votes)
- A point and its reflection over the line x=-1 have two properties: their y-coordinates are equal, and the average of their x-coordinates is -1 (so the sum of their x-coordinates is -1*2=-2).

So (2,3) reflected over the line x=-1 gives (-2-2,3) = (-4,3).(4 votes)

- help, what does he mean when the A axis and the b axis is x axis and y axis?(4 votes)
- They are the same thing: Basically, you can change the variable, but it will still be the x and y-axis.(4 votes)

- i want to know how the xaxis go(4 votes)
- the x-axis and the y-axis is like a tool to help reflect(4 votes)
- Which points are reflections of each other across the y-axis?(4 votes)
- what if you were reflecting over a line like y = 3(3 votes)
- When you reflect over y = 0, you take the distance from the line to the point you're reflecting and place another point that same distance from y = 0 so that the two points and the closest point on y = 0 make a line. The closest point on the line should then be the midpoint of the point and its reflection.

To do this for y = 3, your x-coordinate will stay the same for both points. The y-coordinate will be the midpoint, which is the average of the y-coordinates of our point and its reflection.

(y1 + y2) / 2 = 3

y1 + y2 = 6

y2 = 6 - y1

So to reflect a point (x, y) over y = 3, your new point would be (x, 6 - y).(3 votes)

- how do I reflect when y-1(3 votes)
- I believe that reflection across the Y axis is basically R 180?(3 votes)

## Video transcript

The point negative 8 comma, 5
is reflected across the y-axis. Plot negative 8 comma 5 and its
reflection across the y-axis. So first let's plot
negative 8 comma 5. So its x-coordinate
is negative 8, so I'll just use this
one right over here. So the x-coordinate is negative
8, and the y-coordinate is 5, so I'll go up 5. So the y-coordinate
is 5 right over here. You see negative 8 and 5. We've gone 8 to the left
because it's negative, and then we've gone 5 up,
because it's a positive 5. So we've plotted
negative 8 comma 5. Now we have to plot its
reflection across the y-axis. And so you can imagine if
this was some type of lake or something and you were to
see its reflection, and this is, say, like the moon, you would
see its reflection roughly around here. You would see an equal
distance away from the y-axis. So you would see it at 8 to
the right of the y-axis, which would be at positive 8, and
still 5 above the x-axis. So that's its reflection
right over here. It's reflection is
the point 8 comma 5. Let's do a couple more of these. The point negative
6 comma negative 7 is reflec-- this should say
"reflected" across the x-axis. Plot negative 6 comma
negative 7 and its reflection across the x-axis. So negative 6 comma
negative 7, so we're going to go 6 to the
left of the origin, and we're going to go down 7. So there we go. Negative 6 comma negative
7 is right there. And we are reflecting
across the x-axis. So, once again, if
you imagine that this is some type of a lake,
or maybe some type of an upside-down
lake, or a mirror, where would we think
we see its reflection? Well, its reflection would
be the same distance. We're reflecting
across the x-axis, so it would be the
same distance, but now above the x-axis. So this was 7 below. Now we're going to go
7 above the x-axis, and it's going to be at
the same x-coordinate. So there you have
it right over here. We reflected this
point to right up here, because we reflected
across the x-axis. Let's check our answer. Let's do one more. The point B is a reflection
of point A across which axis? So let's think about
this right over here. This is at the point
negative 6 comma 5. This is at the point
negative 5 comma 6. Let's see. It doesn't look like
it's only one axis. If I were to reflect this
point across the y-axis, it would go all the
way to positive 6, 5. So it would go all the
way right over here. So if I reflect A just across
the y-axis, it would go there. And then if I reflected that
point across the x-axis, then I would end up
at 5 below the x-axis at an x-coordinate of 6. So to go from A to B, you could
reflect across the y and then the x, or you could
reflect across the x, and it would get
you right over here. It would get you to
negative 6 comma 5, and then reflect across the y. So it's really reflecting
across both axes. So we would reflect across the
x-axis and then the y-axis. It would have also
been legitimate if we said the y-axis
and then the x-axis. Let's check our answer. We got it right.