**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.