Class Notes The Coordinate Plane

The Coordinate Plane sometimes called the Cartesian Plane, or coordinate system Class Notes: Vocabulary coordinate plane- a numbered grid (think graph paper) x-axis- a horizontal number line that stretches from the smallest positive number {....-5, -4, -3, -2, 1, 0, 1, 2, 3, 4, 5....}

negative number to the largest

y-axis- a vertical number line that stretches from the smallest negative number to the largest positive number and intersects the x-axis at the zero of both number lines. origin- (0, 0) the point where the x-axis and the y-axis point

intersect and the starting

ordered pair- (x, y) used to describe the location of a point on

the coordinate plane

x-coordinate- (x, _) the first number in the ordered pair found

on the x-axis number line

y-coordinate- (_, y) the second number in the ordered pair found

on the y-axis number line

quadrants- the intersection of the x-axis and the y-axis divide sections known as quadrants. (quad always means four)

the coordinate plane into four

The quadrants are I, II, III, and IV. They are numbered counter-clockwise beginning in the

uppermost right hand corner.

They are always written using Roman numerals. quadrant I- (+, -) All points in quadrant I have a positive y-coordinate.

x-coordinate and a negative

quadrant II- (-, +) All points in quadrant II have a negative y-coordinate.

x-coordinate and a positive

quadrant III- (-,-) All points in quadrant III have a negative y-coordinate.

x-coordinate and a negative

quadrant IV- (+, -) All points in quadrant IV have a positive y-coordinate.

x-coordinate and a negative

The Geometry of the Coordinate Plane Dimension

Axis/Axes

Point Line

x-axis x-axis

Plane (flat surface)

2 Planes (not-flat surface)

Geometry Formula

Measures

Units

Dimensions

Number of Points

Perimeter (add the length of the line all around the shape)

length of the line

units¹

1D

1 2 (minimum)

x-axis, y-axis

Area (length × width)

how much surface is contained inside the perimeter of lines

units²

2D

3 (minimum)

x-axis, y-axis, z-axis

Volume (length × width × height)

measures how much the non-flat surface can contain

units³

3D

4 (minimum)

Note: When a surface is 2D or 2-dimensional, the area formula requires 2 numbers to be multiplied. This always results in units × units = units². When a surface is 3D or 3-dimensional, the volume formula requires 3 numbers to be multiplied. This always results in units × units × units = units³.