Lesson Eight · Unit 3: Geometry and Measurement

Coordinates

Every location on a map, a screen or a game board is described by a pair of numbers. This lesson explains the coordinate plane step by step in English: how to plot points, name quadrants, project points and segments onto the axes, and compute midpoints — with diagrams, worked examples and practice games.

Start here

Learning Outcomes

  • Plot a point on the coordinate plane.
  • Determine the quadrant in which a point is located.
  • Determine the projection of a point on the coordinate axes.
  • Determine the projection of a line segment on the coordinate axes.
  • Determine the coordinates of the midpoint of a line segment.
Begin the lesson
1st (+,+)2nd (−,+)3rd (−,−)4th (+,−)xy-6-6-4-4-2-2224466A(4,3)B(-3,2)C(-4,-3)D(3,-4)

One point in each of the four quadrants.

Big idea

The Coordinate Plane in One Minute

Two axes, one origin

The x-axis and the y-axis are perpendicular number lines meeting at the origin O (0 , 0). Together they form the coordinate plane.

Ordered pairs

A point is written as (x , y). The order matters: (3 , 5) and (5 , 3) are two different points.

Signs decide the quadrant

Reading the signs of x and y tells you instantly which quadrant contains the point, or whether it lies on an axis.

Midpoint of AB, where A(x₁ , y₁) and B(x₂ , y₂) : M = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

Navigate

Lesson Map

Plotting Points & Quadrants

Ordered pairs, signs in each quadrant, points that lie on an axis.

Projections on the Axes

Projection of a point and of a line segment, and how to find its length.

Midpoint of a Line Segment

The midpoint formula, missing endpoints, and quadrilateral proofs.

Activities, Drills & Games

Click-to-plot game, quadrant sprint, midpoint challenge and a full quiz.

Reference

Vocabulary

x-axis
The horizontal number line of the plane.
y-axis
The vertical number line of the plane.
x-coordinate
First number of an ordered pair: horizontal position.
y-coordinate
Second number of an ordered pair: vertical position.
The origin point
O (0 , 0) — where the two axes intersect.
Quadrants
The four regions 1st, 2nd, 3rd and 4th formed by the axes.
Midpoint
The point of a line segment equidistant from its two endpoints.