Math 8: Transformations

ray

(mathematics) a straight line extending from a point

reflection

(mathematics) a transformation in which the direction of one axis is reversed

transformations

A Transformation is a change in the position, size, or shape of a geometric figure. The given figure is called the preimage and the resulting figure is called the image. A transformation maps a figure onto its image. Prime notation is sometimes used to identify image points.

properties

A character or quality that something has. Such as color, height, weight, etc.

enlargement

A dilation with a scale factor greater than 1.

center of rotation

A fixed point around which shapes move in a circular motion to a new position.

line of reflection

A line that a figure is flipped across to create a mirror image of the original figure

coordinates

A pair of numbers used to determine the position of a point on a graph

line segment

A part of a line that has two end points.

coordinate plane

A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.

protractor

A tool used to measure angles

dilation

A transformation that changes the size of an object, but not the shape.

rigid transformation

A transformation that does not change the size or shape of a figure.

sequence

An ordered list or numbers; example: 2,4,6,8,10...

corresponding

Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.

figure

Any point, line, segment, ray, angle, polygon, curve, region, plane, surface, solid, etc

rotation

Definition: a transformation that causes a figure to rotate around a single point changing the orientation of the shape but not its size or shape Context: The artist performed a rotation on the object, turning it around a single point.

congruent

Definition: figures that have the same shape and size; all sides and angles are equal Context: The two boys drew congruent figures that were the same shape and size and had equal sides and angles.

angle

Definition: two rays that share an endpoint Context: The student created an angle by drawing two rays that share an endpoint.

similar (figures)

Figures that have the same shape but not necessarily the same size

parallel lines

Lines in the same plane that do not intersect.

rigid

Not moving. For a construction: where the angles cannot be changed.

reduction

The converting of an expression or equation to its simplest form.

pre-image

The original figure in a transformation

scale factor

The ratio of any two corresponding lengths in two similar geometric figures

scale

The scale is what you mark on the axes. It's the relation between the units you're using, and their representation on the graph i.e., the distance between marks.

proportional

When two quantities always have the same size in relation to each other. In other words they have the same ratio.

two-dimensional figures

a figure that has two basic units of measurement (usually length and width)

vertices

a point where two or more straight lines meet

counterclockwise

in the direction that is opposite of the direction the hands on the clock move

clockwise

in the same direction as the rotating hands of a clock

prime

only divisible by itself and 1

image

the resulting point or set of points under a transformation.

lines

• is straight (no curves), • has no thickness, and • extends in both directions without end (infinitely).