The Four Quadrant Coordinate Plane

Learning Objectives

Identify the x-axis, y-axis, origin, and four quadrants of the Cartesian coordinate plane.

Plot ordered pairs (x, y) with positive and negative coordinates.

Name the quadrant in which a given point lies.

Understand the concept of reflecting a point across the x-axis or y-axis.

Mapping in Two Dimensions

The coordinate plane (or Cartesian plane) is a two-dimensional grid that gives us a way to locate and describe any point on a flat surface. It's like a map for numbers. It is formed by two number lines intersecting at a right angle.

The Anatomy of the Plane

x-axis: The horizontal number line. Positive values are to the right of the center, and negative values are to the left.

y-axis: The vertical number line. Positive values are above the center, and negative values are below.

Origin: The point where the two axes cross. The origin is the 'zero point' and its location is given by the coordinates (0, 0).

Quadrants: The axes divide the plane into four sections. They are numbered using Roman numerals (I, II, III, IV), starting in the top right and moving counter-clockwise.

Quadrant I: Top right (+, +)

Quadrant II: Top left (-, +)

Quadrant III: Bottom left (-, -)

Quadrant IV: Bottom right (+, -)

Plotting Points with Ordered Pairs

Every point on the plane can be described by an ordered pair of coordinates, written as (x, y).

The first number is the x-coordinate. It tells you how far to move along the horizontal x-axis.

The second number is the y-coordinate. It tells you how far to move along the vertical y-axis.

A simple rule is: 'You have to run before you can jump.' Move along the x-axis first, then the y-axis.

Example: Plot the point P = (3, -4)

1.Start at the origin (0, 0).

2.The x-coordinate is +3, so 'run' 3 units to the right.

3.From there, the y-coordinate is -4, so 'jump' 4 units down.

4.Mark the point. This point lies in Quadrant IV.

Reflections on the Plane

A reflection is a transformation that flips a figure over a line of reflection.

Reflecting across the x-axis: When a point is reflected across the x-axis, the x-coordinate stays the same, and the y-coordinate changes its sign.

The reflection of (3, 2) across the x-axis is (3, -2).

Reflecting across the y-axis: When a point is reflected across the y-axis, the y-coordinate stays the same, and the x-coordinate changes its sign.

The reflection of (3, 2) across the y-axis is (-3, 2).

Key Terms

**Coordinate Plane: A two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis.
**Origin: The point (0,0) where the x-axis and the y-axis intersect.
**Ordered Pair: A pair of numbers, (x, y), used to locate a point on a coordinate plane.
**Quadrant: One of the four regions into which the coordinate plane is divided by the x-axis and y-axis.
**Reflection: A transformation that produces a mirror image of a figure or point over a line.