The Coordinate PlaneThe Coordinate PlaneThe The coordinate planecoordinate plane is formed when two number is formed when two number lines (called axis) intersect at right angles.lines (called axis) intersect at right angles.The horizontal axis is called the The horizontal axis is called the x-axisx-axis and the and the vertical axis is called the vertical axis is called the y-axisy-axis. .

The Coordinate PlaneThe Coordinate PlaneThe axis intersect at the The axis intersect at the originorigin and divide the and divide the coordinate plane into four sections called coordinate plane into four sections called quadrantsquadrants..

Quadrant IQuadrant II

Quadrant III Quadrant IV

origin

The Coordinate PlaneThe Coordinate PlaneAn An ordered pairordered pair of numbers identifies the of numbers identifies the location of a point. These numbers are the location of a point. These numbers are the coordinatescoordinates of the point. The coordinate of of the point. The coordinate of the origin is (0,0).the origin is (0,0).

A (-4,3)

(0,0)

The Coordinate PlaneThe Coordinate PlaneNote that point A is 4 units to the left of the y-axis and also Note that point A is 4 units to the left of the y-axis and also 3 units above the x-axis.3 units above the x-axis.

•A (-4,3)

•1•2•3•41•2•3

The numbers –4 and 3 are called the coordinates of point A. The numbers –4 and 3 are called the coordinates of point A. The dot at A is the graph of the point with coordinates (-The dot at A is the graph of the point with coordinates (-4,3).4,3).

x-coordinate y-coordinate

The Coordinate PlaneThe Coordinate PlaneCan you state the coordinates of the Can you state the coordinates of the following points?following points?

AP

BQ

The Coordinate PlaneThe Coordinate PlaneHow did you do?How did you do?

A(5,3)P(-1,5)

B(1,-2)

(-4,-3)Q

The Distance FormulaThe Distance Formula

The distance The distance d between two points between two points A (x1,y1) and and B (x2,y2) is: is:

212

212 )()( yyxxd 2

122

12 )()( yyxxd

B(x2,y2)

(x1,y1)A

In the next lesson, you be learning the basic In the next lesson, you be learning the basic tools of AutoCAD. AutoCAD normally only tools of AutoCAD. AutoCAD normally only uses Quadrant 1 of the coordinate plane.uses Quadrant 1 of the coordinate plane.

A(5,3)P(-1,5)

B(1,-2)

(-4,-3)Q

In Quadrant 1, the X and Y In Quadrant 1, the X and Y coordinates of any number are coordinates of any number are both positive .both positive .Look at the coordinates indicator as you move your mouse around the AutoCAD screen. It shows you the X,Y,Z coordinates of the cursor. They should change as you move the cursor. (If the coordinates do not work, press the F6 key to activate them).

Objects you want to draw can be Objects you want to draw can be located accurately by typing in x located accurately by typing in x and y coordinates. and y coordinates.

For objects like lines, you would specify endpoints.

Objects you want to draw can be Objects you want to draw can be located accurately by typing in x located accurately by typing in x and y coordinates. and y coordinates.

For objects like circles, you would specify the coordinates of the center, and the radius or diameter.