Advanced Geometry - Translations

Distance Formula

To find distance between points.

d=√((x_2-x_1)²+(y_2-y_1)²)

Transformation

A formula used to change or move a figure creating its image.

Translation

Sliding a figure around.

Translation Vectors

〈x,y〉

Reflection

Flipping a figure over a line.

Reflection : over x-axis

(x,y) → (x,-y)

Reflection : over y-axis

(x,y) → (-x,y)

Reflection : over y=x

(x,y) → (y,x)

Reflection : over y=-x

(x,y) → (-y,-x)

Midpoint Formula

m=((x₁+ x₂)/2, (y₁ + y₂)/2)

Point Slope Formula

y - y₁ = m(x - x₁)

Rotation

Spinning/turning about a point. (0,0)

Counter Clockwise

90° → (-y,x)

Clockwise

270° → (-y,x)

Counter/Clockwise

180° → (-x,-y)

Counter Clockwise

270° → (y,x)

Clockwise

90° → (y,x)

Composition

More than one transformation.

Composition consists of…

Translating and reflecting, or vice versa. Order always matters.