Lesson 1

Table of Contents

Lesson 1

RENE' DESCARTES

CARTESIAN COORDINATES

The scaling on each axis is symmetric about the origin.

The ordered pair (a,b) corresponds to the point where the perpendicular to the x-axis at a crosses the perpendicular to the y-axis at b.

a is the x-coordinate of P. b is the y-coordinate of P. (a,b) is the coordinate pair of the point P.

The assignment of coordinates is a one-to-one correspondence between the points of the plane and the set of all ordered pairs of real numbers.

Directions and Quadrants

NOTE...

...NOTE

NOTATION

ILLUSTRATION

Increments

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Distance Formula

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EXAMPLE

Circles centered at the origin

Unit Circle

Midpoint

EXAMPLE

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Slopeof a non-vertical line

ILLUSTRATION

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EXAMPLE

Angle of Inclinationof a line that crosses the x-axis

Angle of Inclination

ILLUSTRATION

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Perpendicular Lines

EXAMPLE

Equation for a Line

Horizontal Line

Vertical Line

ILLUSTRATION

Point-Slope Equation

EXAMPLE

EXAMPLE

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...SOLUTION

Slope-Intercept Equation

EXAMPLE

General Linear Equation

EXAMPLE

EXAMPLE

Lines through the origin

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MATH 1910

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