Coordinates

Definition

Coordinates are pairs of numbers used to locate points on a graph or a plane. They are typically written as (x, y), where x represents the horizontal position and y represents the vertical position.

Graphing on the Coordinate Plane

The coordinate plane consists of a horizontal x-axis and a vertical y-axis. The point where the two axes intersect is called the origin and has the coordinates (0, 0). To plot a point on the coordinate plane, you move a certain number of units to the right or left along the x-axis, and then a certain number of units up or down along the y-axis.

Quadrants

The coordinate plane is divided into four quadrants, labeled I, II, III, and IV, which are numbered counterclockwise starting from the top right quadrant. The signs of the x and y coordinates determine the quadrant in which a point lies.

Distance and Midpoint Formulas

The distance between two points with coordinates (x1, y1) and (x2, y2) can be found using the distance formula:
√((x2 - x1)^2 + (y2 - y1)^2)

The midpoint between two points with coordinates (x1, y1) and (x2, y2) can be found using the midpoint formula:
((x1 + x2)/2, (y1 + y2)/2)

Study Guide

1. Understand the concept of coordinates and how to read them as (x, y).
2. Be able to plot points on the coordinate plane and identify their coordinates.
3. Learn the four quadrants of the coordinate plane and understand how to determine the quadrant in which a point lies based on its coordinates.
4. Practice using the distance and midpoint formulas to find the distance and midpoint between two points on the coordinate plane.
5. Complete practice problems to reinforce the understanding of coordinates and the coordinate plane.

[Coordinates] Related Worksheets and Study Guides:

• CoordinatesMathematics • Fourth Grade
• Plot PointsMathematics • Fifth Grade
• Area of Coordinate PolygonsMathematics • Sixth Grade