Transformations in Coordinate Geometry

Front

(x, y) --> (-y, x)

Back

90 degree rotation CCW about the origin

Front

(x, y) --> (x + a, y + b)

Back

Translation

a units to the right and b units up

Front

(x, y) --> (-x, y)

Back

Reflection over the y-axis

Front

(x, y) --> (x, -y)

Back

Reflection over the x-axis

Front

(x, y) --> (x cos(θ) - y sin(θ), x sin(θ) + y cos(θ))

Back

Rotation by angle θ about the origin

Front

(x, y) --> (kx, ky) where k > 1

Back

Dilation with scale factor k

Front

What is the image of the point (2, 3) after (x, y) --> (x + 2, y - 1)?

Back

(4, 2)

Front

What is the image of the point (-7, 1) after (x, y) --> (-x, y)?

Back

(7, 1)

Front

What is the image of the point (8, 1) after (x, y) --> (x, -y)?

Back

(8, -1)

Front

What are the requirements of a square?

Back

All sides equal, opposite sides parallel, adjacent sides perpendicular.