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Lesson 4: Reflections

# Reflecting points

We can plot points after reflecting them across a line, like the x-axis or y-axis. Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right.

## Want to join the conversation?

• What does prime mean when for example they say C prime?
• In the context of geometric transformations, the prime symbol (') denotes the image of a point as a result of a transformation. For example, point A' is the image of point A, point B' is the image of point B, and point C' is the image of point C.

Eventually, you might see prime symbols in other mathematical contexts as well. For example, in calculus, if f is a function, then f' denotes the derivative (instantaneous rate of change) of the function f.
• not as bad as rotating...rotation confuses me
• 90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
• Is there a video that shows how to reflect a point over a diagonal line? I am really confused because I thought that there was a formula to do so.
• how do you identify the reflection of -2,6 ?
• Depends what axis you are reflecting over, if you are reflecting over x axis, change the y positive or negative sign to the opposite sign, if it reflects over y axis, change the sign of the x.
Hope this helps
• if it helps reference stranger things. the Upside Down mirrors the actual world. Then imagine Will Byers from stranger things as a shape/ figure undergoing reflection. Simplified, i would describe a trip to the Upside Down a reflection in mathematical terms
• can i get a little bit of explanation?
• Some basic rules:

- Reflection over x-axis:
(x, y) ---> (x, -y)
- Reflection over y-axis
(x, y) ---> (-x, y)
- Reflection over line where y = x
(x, y) ---> (y, x)
- Reflection over line where y = -x
(x, y) ---> (-y, -x)
• Thanks! there's actually a way to do it algebraically too, if you don't know it already you'll need it: Across the x-axis -(x,y)- (x,-y)
Across the y-axis- (x,y) - (-x, y)
Just follow this rule and you won't even need a graph to know a reflection!
• Is reflecting the same thing as rotating 180 degrees about point "x" for example?
• That depends on the shape. In the case of a square, for example, you could rotate it 90 degrees about the center and get the same thing. However, if the shape does not have a line of symmetry, and is rotated 180 degrees around "point x", you might not get the same thing.
• This was fairly easy thank you for making this so i can understand it better.
• are you exposed to be in high school ? if so I'm in elementary school
• You don't have to be in a specific grade to learn the concepts. This is done on purpose so students can learn at their own pace. With that said, don't feel bad if you do not understand some of the stuff at this level.