1. Transformations on a Coordinate Plane
By: Audrey Orr
Geometry 1st Period

2. This Presentation Is About…
the three different types of transformations and their functions. I will also describe how to plot and construct them.

3. Transformations
A transformation is when there is a change in the position, size, or shape of a figure.
The figure before the transformation is called the preimage, and the transformation after is called the image.
Arrow notation (→) is the symbol to describe a transformation (ex. Triangle ABC → Triangle A’B’C’).
Primes (‘) are used to show the image.

4. Reflection
Reflection (or flip) is a type of transformation that reflects across the line, also called the line of reflection.
Each point and its image are the same distance from the line of reflection.
Example:

5. Rotation
A rotation (or turn) is a transformation at a point (center of rotation). This is the only point that stays; the other points rotate to new points.
Again, each point and its image are the same distance from the point.
Example:

6. Translation
A translation (or slide) is the type of transformation in which all the points of a figure move the same distance in the same direction.
Example:

7. How To Construct a Reflection
First, plot three or more points on a coordinate plane that can form a figure.
The highlighted portion is the preimage:

8. How To (cont.)
Next, plot new points that are the same distance apart. (Ex. Point O is the same distance from Point O’, M is the same distance from Point M’.)
The highlighted portion is the image:

9. How To Construct a Rotation
Again, you have to plot three or more points on a coordinate plane that creates a figure.
The highlighted portion is the preimage:

10. How To (cont.)
After plotting your three points, mark one point that you want to keep and rotate the others the exact same distance as each other.
The highlighted portion is the image:

11. How To Construct A Translation
For the last time (I promise) plot three or more points that form a figure.
The highlighted portion is the preimage:

12. How To (cont.)
After constructing a figure, you can plot the image anywhere on the plane, as long as all the points are the same distance from each other. (Remember, Point A would be the same distance from Point A’ as B would be to B’)
The highlighted portion is the image:

13. What type of transformation is this?
Quiz Time!
What type of transformation is this?

14. That’s Right!
It is a translation.

15. What type of transformation is this?
Next Question!
What type of transformation is this?

16. Yay!
It is a rotation.

17. It’s Time To Talk About What We’ve Learned Today…
This presentation was about the three different types of transformations: reflection, rotation, and translation. We learned that each one has a different function and different way of construction.

18. Thank You!
This concludes my presentation on the different types of transformation of figures on a coordinate plane.