A reflection is a transformation that flips a shape over a mirror line, producing a mirror image.
Common mirror lines:
- x-axis
- y-axis
- x = k (vertical line)
- y = k (horizontal line)
- y = x (diagonal line)
Reflection Rules
|
Mirror Line |
Mapping Rule |
|
x-axis |
(x, y) → (x, −y) |
|
y-axis |
(x, y) → (−x, y) |
|
y = x |
(x, y) → (y, x) |
|
y = −x |
(x, y) → (−y, −x) |
Worked Example 1
Reflect point P(6, 4) in the y-axis.
New position: (−6, 4)
Worked Example 2
Reflect triangle ABC with coordinates:
A(2,1), B(4,1), C(4,4)
in the y-axis.
Images:
- P(-3,5)
- Q(-2,−2)
- R(-4,2)