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)
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