Transformation Cheat Sheet
Transformation
Preimage
Coordinates
Image
Coordinates
Description
Translation
(𝑥, 𝑦)
(𝑥 + / − 𝑛, 𝑦 + / −
Add or subtract the number of
units(𝑛)the preimage
was moved.
𝑥 + 𝑛 = right
𝑥 − 𝑛 = left
𝑦 + 𝑛 = up
𝑦 − 𝑛 = down
Reflection
(𝑥, 𝑦)
x-axis = (𝑥, − 𝑦)
y-axis = (− 𝑥, 𝑦)
● Reflect the image over the
x-axis, the x coordinate
stays the same, and the y
is the opposite.
● Reflect the image over the
y-axis, the y coordinate
stays the same, and the x
is the opposite
Rotation
(𝑥, 𝑦)
clockwise:
90° = (𝑦, − 𝑥)
180° = (− 𝑥, − 𝑦)
270° = (− 𝑦, 𝑥)
90° = switch original coordinates;
take the opposite of 𝑥
180° = take the opposite of the
original coordinates
270° = switch original coordinates;
take the opposite of 𝑦
Dilation
(𝑥, 𝑦)
(𝑘𝑥, 𝑘𝑦)
Multiply each coordinate by the
scale factor (𝑘)
Enlarge image = 𝑘 > 1
Shrink image = 𝑘 < 1