Translations
Standard
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Goals for this section:
To understand that translations are just ways to describe moving something. Generally we'll just consider moving horizontally (x-values) and vertically (y-values).
Important Notation
Preimage
The original figure
➝
Translates to
Image
The resulting figure
Rigid Motion
An object moves, but it does not change in size. So the preimage has been moved around, flipped, or rotated but it's still the same shape with the same size!
Naming Images and Corresponding Parts
Naming Images
HIJK is the preimage
So name the image.
This looks like a reflection! Like as if HIJK was staring at itself in the mirror. So the image of HIJK must be ABCD.
Corresponding Parts
Order matters!
Example
ΔABC ➝ ΔA’B’C’
This says, "triangle ABC translates to triangle A prime, B prime, C prime."
The first letter in the preimage corresponds with the first letter of the image, and so on. The order of the letters in the preimage should match with the order of the letters of the image.
Example
ΔNID ➝ ΔSUP
So for this example:
- N corresponds with S
- I corresponds with U
- D corresponds with P
Again, the order matters!
Applying Translations
"T" stands for translation. This says, "The translation of ΔABC is ΔA'B'C'.
This is the same thing, but it's more specific.
- The x means that ΔABC moved x units to the left or right.
- The y means that ΔABC moved y units up or down.
So therefore, this means that ΔA'B'C' is the image of ΔABC when moved x units to the left/right and y units up/down.
Example
ΔABC moved 3 units to the left (because negative) and moved 2 units up. The resulting image is ΔA'B'C'.
So here's an example of the transformation.
The black triangle labeled ABC is translated 3 units to the left and 2 units up.
