Co-ordinate Geometry
281. Coordinates of Points · Mastering the Cartesian Plane
The coordinates (x, y) uniquely define the point's position relative to the axes.
A point's coordinates (x, y) give its position: x is how far right or left of the y-axis, and y how far up or down from the x-axis. Each point has exactly one ordered pair, and each ordered pair one point.
What this lesson covers
Try to break it
Drag P around. The x-coordinate is P's signed horizontal distance from the y-axis (positive right, negative left). The y-coordinate is the signed vertical distance from the x-axis (positive up, negative down). Drag P to the origin and both coordinates read 0; drag P along an axis and one of them reads 0.
How you build it
Plot a point from its coordinates on the graduated plane.
- Point tool: plot the point (-2, -3). Count 2 to the left along x, then 3 down along y, and click that grid spot.
The proof, step by step
Prove that the coordinates (x, y) fix the position of a point uniquely.
- Draw perpendiculars from P to both axes.
- Measure the distances from the origin along each axis.
- The distances form the ordered pair (x, y).
Worked example
In a Cartesian plane, a point P is located 150 units to the right of the y-axis and 100 units below the x-axis. What are the coordinates of P?
Right means positive x, down means negative y. So the coordinates are (150, -100).
- (150, 100)
- (150, -100) — correct
- (-150, 100)
- (-150, -100)