Cartesian Coordinate System

In a cartesian coordinate plane, any point can be represented by a pair of numerical coordinates. The horizontal line is called the x-axis, and the vertical line is called the y-axis. The point at which both the axes meet, (0, 0), is called the origin.

cartesian-coordinate

Ordered Pair: Also known as a coordinate pair, this duo is the set of two values that expresses the distance a point lies from the origin. The horizontal (x) coordinate is always listed first, and the vertical (y) coordinate is listed second.

x-intercept: The value of x where a line, curve, or some other function crosses the x-axis. The value of y is 0 at the x-intercept. The x-intercept is often the solution or root of an equation.

y-intercept: The value of y where a line, curve, or some other function crosses the y-axis. The value of x is 0 at the y-intercept.

Slope: Slope measures how steep a line is and is commonly referred to as the rise over the run.

Quadrants

The intersection of the x- and y-axes forms four quadrants on the coordinate plane.

  • All points in Quadrant I have a positive x value and a positive y value.
  • All points in Quadrant II have a negative x value and a positive y value.
  • All points in Quadrant III have a negative x value and a negative y value.
  • All points in Quadrant IV have a positive x value and a negative y value.
  • All points along the x-axis have a y value of 0.
  • All points along the y-axis have an x value of 0.

Distance Formula

Assume you have two points, A (x1, y1) and B (x2, y2), on a line. The formula to find the distance between A and B is