8.10C/8.3C Transformation Rules in Geometry

Front

Translations: Slide

Back

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.

Front

Reflection: A flip over the x-axis or y-axis.

Back

Reflection Rules:

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

Front

Rotation rules describe how to rotate/turn/spin a point around the origin.

Back

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).

Front

Enlargement occurs when the scale factor (a) is greater than 1.

The coordinates are multiplied by the scale factor

Back

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).

Front

Reduction occurs when the scale factor (a) is between 0 and 1.

The coordinates are multiplied by the scale factor

Back

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).

Front

Translations

Back

Rigid motion that is a "slide."

Front

Reflections

Back

Rigid motion that is a "flip."

Front

Rotations

Back

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

Front

Transformations

Back

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

Front

Congruent Figures

Back

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.