Transformation Rules

Reflection over the x-axis

(x, y) → (x, -y)  x stays the same, opposite of y

Reflection over the y-axis

(x, y) →  (-x, y) opposite of x, y stays the same

Reflection over a vertical line x = #

Draw a vertical line at that number, count the number of spaces to the vertical line

Reflection over a horizontal line y = #

Draw a horizontal line at that number, count the number of spaces to the horizontal line

Reflection over the line y = x

(x, y) → (y, x) switch x & y

Rotation 90 degrees COUNTERCLOCKWISE

(x, y) → (-y, x) switch x & y, make y it’s opposite

Rotation 90 degrees CLOCKWISE

(x, y) → (y, -x) switch x & y, make x it’s opposite

Rotation 180 degrees 

(x, y) → (-x, -y) opposite of x & opposite of y

Translations

If you move to the left you subtract.

If you move to the right you add.

If you move up you add.

If you move down your subtract.

Dilations

Rule: (x,y) → (Kx, Ky) K is the scale factor.  You multiple x and y by the scale factor.