Coordinate Plane

The coordinate plane is a two-dimensional plane formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. The point where the x-axis and y-axis intersect is called the origin, denoted as (0, 0).

Quadrants

The coordinate plane is divided into four regions called quadrants. The quadrants are labeled using Roman numerals in a counterclockwise direction starting from the top right quadrant.

Quadrant I: The top right quadrant where both x and y-coordinates are positive.
Quadrant II: The top left quadrant where x-coordinate is negative and y-coordinate is positive.
Quadrant III: The bottom left quadrant where both x and y-coordinates are negative.
Quadrant IV: The bottom right quadrant where x-coordinate is positive and y-coordinate is negative.

Ordered Pair

In the coordinate plane, a point is represented by an ordered pair (x, y), where x is the horizontal distance from the y-axis (positive to the right, negative to the left) and y is the vertical distance from the x-axis (positive upwards, negative downwards).

Distance Formula

The distance between two points in the coordinate plane can be found using the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Midpoint Formula

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Graphing on the Coordinate Plane

To graph a point on the coordinate plane, start at the origin and move along the x-axis and then up or down along the y-axis to the point indicated by the ordered pair.

Study Guide

What are the two axes that form the coordinate plane?
What is the point of intersection of the x-axis and y-axis called?
How are the quadrants labeled in the coordinate plane?
What is an ordered pair and how is it represented on the coordinate plane?
State the distance formula and explain its components.
State the midpoint formula and explain its components.
How do you graph a point on the coordinate plane?

These questions and concepts will help you understand and master the topic of the coordinate plane. Good luck with your studies!

◂Math Worksheets and Study Guides Eighth Grade. Patterns in geometry

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Examine the congruence, similarity, and line or rotational symmetry of objects using transformations.