Foundations

The xy-Plane & Coordinates

Every line, parabola, and circle on the SAT lives here. Master the navigation of the coordinate plane first.

The Cartesian Coordinate System

xy-Plane Diagram

The xy-plane is formed by two perpendicular number lines:

  • 👉 x-axis: The horizontal number line.
  • 👉 y-axis: The vertical number line.
  • 👉 Origin (0,0): Where the two axes intersect.

The Four Quadrants

The axes divide the plane into four regions called Quadrants. They are numbered counter-clockwise starting from the top-right.

Quadrant I
(+, +)

Right & Up

Quadrant II
(-, +)

Left & Up

Quadrant III
(-, -)

Left & Down

Quadrant IV
(+, -)

Right & Down

Ordered Pairs: (x, y)

To locate any point, we use an ordered pair of numbers called coordinates.

Example: Point P(3, 2)
  • 1. Start at the **Origin (0,0)**.
  • 2. Move **right 3 units** (x = 3).
  • 3. Move **up 2 units** (y = 2).

💡 Tip: X always comes before Y. Just like in the alphabet!