Intermediate Algebra chapter 3 part 1

The Cartesian Coordinate System
Chapter 3

Cartesian Coordinates--Overview

• Locate points in 2-D by specifying where the point is relative to the Origin.
• Any point may be specified by an ordered pair (described below).
• The horizontal line labeled "x" is the x-axis.
• The vertical line labeled "y" is the y-axis.
• Quadrants are regions of the plane relative to the origin.

  Quadrant I: x > 0 and y > 0

  Quadrant II: x < 0 and y > 0

  Quadrant III: x < 0 and y < 0

  Quadrant IV: x > 0 and y < 0

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Ordered Pairs (x, y)

• Any point in 2-D may be located by an ordered pair (x, y).
• The x-coordinate, x, is the value on the x-axis vertically above or below the point.
• The y-coordinate, y, is the value on the y-axis horizontally right or left of the point.
• The order is that the x-coordinate is listed first and the y-coordinate is listed second.

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Distance Formula

The distance formula gives the distance, d, between 2 given points (x₁, y₁) and (x₂, y₂).Distance is always non-negative.

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Midpoint Formula

The midpoint formula gives an ordered pair that is the point halfway between 2 given points (x₁, y₁) and (x₂, y₂).