Connecting Algebra with the Coordinate Plane

First, let’s take a look at….

A little history

A little history René Descartes (1596-1650) philosopher mathematician joined algebra and geometry credited with--- Cartesian plane

The year is 1630. Lying on his back, French mathematician René Descartes, watches a fly crawl across the ceiling. Suddenly, an idea comes to him. He visualizes two number lines, intersecting at a 90° angle. He realizes that he can graph the fly's location on a piece of paper. Descartes called the main horizontal line the x-axis and the main vertical line the y-axis. He named the point where they intersect the origin.

Descartes represented the fly's location as an ordered pair of numbers. The first number, the x-value, is the horizontal distance along the x-axis, measured from the origin. The second number, the y-value, is the vertical distance along the y-axis, also measured from the origin.

Now, let’s take a look at…

Cartesian plane Formed by intersecting two real number lines at right angles

Cartesian plane Horizontal axis is usually called the x-axis

Cartesian plane Vertical axis is usually called the y-axis

Cartesian plane Also called: x-y plane rectangular coordinate system

Cartesian plane II I Divides into Four Quadrants and… III IV

of the two axes is called the origin Cartesian plane The intersection of the two axes is called the origin

The quadrants do not include the axes Cartesian plane II I Math Alert The quadrants do not include the axes III IV

A point on the x or y axis is not in a quadrant Cartesian plane II I Math Alert A point on the x or y axis is not in a quadrant III IV

x-y plane is associated with an ordered pair, (x,y) Cartesian plane Each point in the x-y plane is associated with an ordered pair, (x,y) (x,y) (x,y) (x,y) (x,y)

Cartesian plane The x and y of the ordered pair, (x,y), are called its coordinates (x,y) (x,y) (x,y) (x,y)

There is an infinite amount of points in the Cartesian plane Math Alert There is an infinite amount of points in the Cartesian plane

The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers. COORDINATE PLANE The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect. ORIGIN

Take note of these graphing basics

Cartesian plane Always start at (0,0)---every point “originates” at the origin

---remember the directions of both the x and y Cartesian plane y In plotting (x,y) ---remember the directions of both the x and y axis x

Cartesian plane (x,---) x-axis goes left and right

Cartesian plane (---,y) y-axis goes up and down

Now, let’s look at graphing…

Cartesian plane Start at (0,0) ( , ---) Move right 2 +

Cartesian plane (---, ) (---, 1) Move up 1 +

Now, let’s look at graphing…

Cartesian plane Start at (0,0) ( , ---) Move right 4 +

Cartesian plane (---, ) (---, -2) Move down 2 -

Cartesian plane Start at (0,0) ( , ---) Move left 3 -

Cartesian plane + (---, ) (---, 5) Move up 5

Cartesian plane Start at (0,0) (none,---) No move right or left

Cartesian plane + (0, ) (---, 4) Move up 4

Now, let’s look at graphing…

Cartesian plane Start at (0,0) ( ,---) Move left 5

Cartesian plane ( ---, 0) No move up or down

Points in Quadrant 2 have negative x but positive y coordinates. Points in Quadrant 1 have positive x and positive y coordinates. To make it easy to talk about where on the coordinate plane a point is, we divide the coordinate plane into four sections called quadrants. Points in Quadrant 3 have negative x and negative y coordinates. Points in Quadrant 4 have positive x but negative y coordinates.

Cartesian plane Approximate the coordinates of the point--- Directions: Approximate the coordinates of the point--- Or what is the ‘(x,y)’of the point?

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Directions: Approximate the coordinates of the point

Cartesian plane Find the coordinates of the point two units Directions: Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis

Cartesian plane Find the coordinates of the point two units Directions: Find the coordinates of the point two units to the left of the y-axis and five units above the x-axis

the point on the x-axis and three units to the left of the Cartesian plane Directions: Find the coordinates of the point on the x-axis and three units to the left of the y-axis

a point on the x-axis and three units to the left of the Cartesian plane Directions: Find the coordinates of a point on the x-axis and three units to the left of the y-axis

You can do this!