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# Reflecting points in the coordinate plane

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.