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## Geometry (all content)

### Course: 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
• help, what does he mean when the A axis and the b axis is x axis and y axis?
• They are the same thing: Basically, you can change the variable, but it will still be the x and y-axis.
• How would you reflect a point over the line y=-x?
• It works just like any line, graph it and follow the line reflection rules. :)
• i want to know how the xaxis go
• X-axis goes left and right, when reflecting you will need to go up or down depending on the quadrant. if it is on one of the bottom quadrants, it will go up, if it is on the top quadrants, it will go down. hope this helps, even if this is 3 years later.
(1 vote)
• What happens if it tells you to plot 2,3 reflected over x=-1
• 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).
• what if you were reflecting over a line like y = 3
• 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).
• the x-axis and the y-axis is like a tool to help reflect
• Which points are reflections of each other across the y-axis?
• X-axis goes left and right, when reflecting you will need to go up or down depending on the quadrant. if it is on one of the bottom quadrants, it will go up, if it is on the top quadrants, it will go down. hope this helps, even if this is 3 years later.
(1 vote)
• (2,-3) is reflected over the y-axis. what is the new coordinates of the point after its reflection?
• When a point is reflected along the y axis, the X coordinate becomes the opposite number and the y coordinate stays the same.

Likewise, when a point is reflected along the X axis, the X coordinate stays the same and the y coordinate becomes the opposite.

(2,-3) reflected along the y axis
The Y coordinate stays the same, in this case it is -3
The x coordinate is opposite.
What is the opposite of 2?
-2

So, the answer would be (-2,-3)

Hope this helps!