Coordinate plane, ordered pairs, plotting points
Middle School Bridge • 6-8
Maps use a grid system to identify locations: "Row 3, Column 5" pinpoints a single square. The coordinate plane works the same way, using two numbers to identify any point in a flat space. This system, invented by the mathematician Rene Descartes, connects algebra and geometry -- allowing us to visualize equations and data.
The coordinate plane is formed by two perpendicular number lines:
The axes divide the plane into four quadrants:
| Quadrant | x | y | Location |
|---|---|---|---|
| I | + | + | Upper right |
| II | − | + | Upper left |
| III | − | − | Lower left |
| IV | + | − | Lower right |
Every point on the coordinate plane is described by an ordered pair (x, y). The first number tells you how far to move horizontally from the origin, and the second tells you how far to move vertically.
Plot the point (3, 4).
Plot the point (-2, -5).
A point lies 4 units left of the origin and 3 units above it. What are its coordinates?
Moving left means negative x: x = -4. Moving up means positive y: y = 3. The ordered pair is (-4, 3), which is in Quadrant II.
The order in an ordered pair matters! The point (3, 5) is NOT the same as (5, 3). Always go horizontal first (x), then vertical (y). A helpful memory trick: you walk along the hallway (x) before you take the elevator (y).
If a point has y = 0, it lies on the x-axis (e.g., (5, 0)). If a point has x = 0, it lies on the y-axis (e.g., (0, -3)). Points on the axes are not in any quadrant.
1. In which quadrant is the point (-7, 2)?
x is negative and y is positive, so the point is in Quadrant II.
2. What are the coordinates of the origin?
(0, 0).
3. A point is 6 units right and 2 units below the origin. Give its ordered pair and quadrant.
(6, -2), Quadrant IV.
4. Plot and label the following points: A(2, 5), B(-3, 1), C(0, -4), D(4, -2). Which points are in Quadrant I?
A(2, 5) is in Quadrant I (both coordinates positive). B(-3, 1) is in Quadrant II. C(0, -4) is on the y-axis (not in any quadrant). D(4, -2) is in Quadrant IV. Only point A is in Quadrant I.
5. If you reflect the point (3, -7) across the x-axis, what are the new coordinates?
Reflecting across the x-axis changes the sign of y. New point: (3, 7).
The coordinate plane uses two perpendicular axes to locate any point using an ordered pair (x, y). Move horizontally for x and vertically for y. The four quadrants are determined by the signs of the coordinates. Points on the axes have one coordinate equal to zero. Always remember: x comes first, y comes second.