Symmetry and Transformations Math Quiz

Line symmetry

A figure has line symmetry if there exists a line that divides the figure into two equal parts, such that one can be mapped onto the other by folding across the line of symmetry.

Point symmetry

A figure has point symmetry if it can be rotated 180˚ around a central point and maps back onto itself exactly.

Translation

• Moves a figure vertically or horizontally

• h represents the horizontal shift

• k represents the vertical shift

Reflection

• A flip over a line called the line of reflection

• Each point and its image are the same distance from the line of reflection

• A reflection is also an example of a rigid motion

Rotation

• A turn around a fixed point called the center of rotation

• The figure rotates at a specific angle and direction

• Though the figure can rotate around a fixed point, the most common center of rotation is the origin.

Rules of rotation: 90˚ (counterclockwise)

(x,y) —> (-y,x)

Rules of rotation: 180˚

(x,y) —> (-x,-y)

Rules of rotation: 270˚ (counterclockwise)

• Is the same as 90˚ clockwise

• (x,y) —> (y,-x)

Dilation

• A dilation is a reduction or enlargement of a figure with respect to a fixed point, called the center of dilation

• A dilation is an example of a non-rigid transformation in that it does no preserve congruency

• A dilation produces similar figures

• All corresponding angles are congruent, and all corresponding sides are proportional

Scale factor in dilation

• The scale factor indicates how much the figure will enlarge or reduce

• Variable for scale factor: k

When ______ the dilation is an enlargement

k > 1

When ______ the dilation is an reduction

k < 1

What distinguishes the pre-image from the image in dilation?

The image is labeled with an apostrophe after each of the letters that label it’s points.

Dilation rule

If P(x,y) is the pre-image of a point, then its image after dilation centered at the origin (0,0) with scale factor k will follow the rule: multiply the coordinates by the scale factor