Transformations in the Coordinate Plane Module Overview

Introduction

Flowers of life image Geometry is the branch of mathematics that is concerned with points, lines, planes, shapes and figures. In this unit, you will learn the relationship between each of those terms! You will also learn how to manipulate figures to create new figures through rotations, reflections & transformations. Geometry is used in the development of video games, engineering, architecture, and medical imaging, to name a few!

Essential Questions

What are the undefined terms essential to any study of geometry?
How do you determine the type of transformation that has occurred?
What effects do transformations have on geometric figures?
How do we define and create geometric transformations?
Which transformations create isometries?
How do we translate geometric figures in the coordinate plane?
How do we reflect, rotate and translate points in a coordinate plane?
How are reflections and rotations similar and different?
How can we describe/represent a transformation (or series of transformations) that take place in the coordinate plane?
How can the coordinate plane help me understand properties of reflections, translations and rotations?

Key Terms

The following key terms will help you understand the content in this module.

Angle - A figure created by two distinct rays that share a common endpoint (also known as a vertex). $LaTeX: \angle ABC\:or\:\angle B\:or\:\angle CBA$ indicate the same angle with vertex B.

Angle of Rotation - The degree a figure is rotated (clockwise or counterclockwise) about a fixed point, such as the origin.

Bisector - A point, line or line segment that divides a segment or angle into two equal parts.

Circle - The set of all points equidistant from a point in a plane.

Congruent - Having the same size, shape and measure. $LaTeX: \angle A\:\cong\angle B$ indicates that angle A is congruent to angle B.

Corresponding angles - Angles that have the same relative position in geometric figures.

Corresponding sides - Sides that have the same relative position in geometric figures.

Endpoint - The point at each end of a line segment or at the beginning of a ray.

Image - The result of a transformation.

Intersection - The point at which two or more lines intersect or cross.

Isometry - A rigid transformation that preserves the size and shape of the figure. A distance preserving map of a geometric figure to another location using a reflection, rotation or translation. $LaTeX: M\:\longrightarrow M^1$ indicates an isometry of the figure M to a new location M'. M and M' remain congruent.

Line - One of the undefined terms of geometry that represents an infinite set of points with no thickness and its length continues in two opposite directions. $LaTeX: \overleftrightarrow{AB}$ indicates a line that passes through the points A and B.

Line segment - A part of a line between two points on the line. $LaTeX: \overline{AB}$ indicates the line segment between points A and B.

Parallel lines - Two lines are parallel if they lie in the same plane and do not intersect. equation image indicator $LaTeX: \overleftrightarrow{AB}\parallel \overleftrightarrow{CD}$ indicates that line AB is parallel to line CD.

Perpendicular lines - Two lines are perpendicular if they intersect to form right angles. $LaTeX: \overleftrightarrow{AB}\bot \overleftrightarrow{CD}\$ equation image indicator indicates that line AB is perpendicular to line CD.

Point - One of the basic undefined terms of geometry that represents a location. A dot is used to symbolize it and it is thought of as having no length, width or thickness.

Pre-image - A figure before a transformation has taken place.

Ray - A part of a line that begins at a point and continues forever in one direction. $LaTeX: \overrightarrow{AB}$ indicates a ray that begins at point A and passes through point B, and continues on, infinitely.

Reflection - A transformation of a figure that creates a mirror image, "flips," over a line.

Reflection Line (or line of reflection) - A line that acts as a mirror so that corresponding points are the same distance from the mirror.

Rotation - A transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90° clockwise.

Transformation - The mapping, or movement, of all points of a figure in a plane according to a common operation, such as a translation, reflection or rotation.

Translation - A transformation that slides each point of a figure the same distance in the same direction.

Vertex - The location at which two lines, line segments or rays intersect.

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