8.10C/8.3C Transformation Rules in Geometry

Translations Rule: (x, y) --> (x + a, y + b);

a and b are numbers.

Positive direction: x: right, y: up.

Negative direction: x: left, y: down.

Reflection Rules:

Reflection over x-axis: (x, y) --> (x, -y); Reflection over y-axis: (x, y) --> (-x, y).

Rotation Rules:

Rotation 90° counterclockwise and 270° clockwise: (x, y) --> (-y, x);

Rotation 270° counterclockwise and 90° clockwise: (x, y) --> (y, -x);

Rotation 180°: (x, y) --> (-x, -y).

Dilation Rules:

Enlargement - a > 1 (a is greater than 1). Examples: (x, y) --> (ax, ay).

If a = 3: (x, y) --> (3x, 3y).

If a = 5/4: (x, y) --> (5/4x, 5/4y).

Dilation Rules:

Reduction - 0 < a < 1 (a is greater than 0 and less than 1).

Examples: (x, y) --> (ax, ay).

If a = 0.3: (x, y) --> (0.3x, 0.3y).

If a = 1/2: (x, y) --> (1/2x, 1/2y).

Rigid motion that is a "slide."

Rigid motion that is a "flip."

Rigid motion that is a "spin" or "turn."

Mapping or movement (rigid motion) of a figure on a coordinate plane.

Rigid motions like translations, reflections, and rotations that preserve all shape and sizes after transformations are performed. Angles measurements and side lengths stay the same.