Introduction to Finding Pythagoras

Graphing with CoordinatesGraphing with Coordinates

on the Cartesian Planeon the Cartesian Plane

Ancient Math Geek, Rene Descartestook a number line and ran it left to right and called it the x-axis.

The smaller numbers are on the left of the number line and the higher numbers are to the right of the line.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Ancient Math Geek, Rene Descartesthen took a number line and ran it up and down and called it the y-axis.

The smaller numbers are down the line and the higher numbers are up on the line.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

4

3

2

1

0

-1

-2

-3

-4

By the way, how many points are on my number line?

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

There are an infinite number of points on any number line. Between each whole number are countless fractions and decimals. Also each line continues on to the right or up to

infinity ∞ and to the left or down to negative infinity -∞ - the line never stops.

The Cartesian Plane: x & y -axisy-axis

x-axis

Remember too, the x-axis is for the INDEPENDENT variable & the y-axis is for the DEPENDENT variable.

The Cartesian Plane: originy-axis

x-axis

Quadrant IQuadrant II

Quadrant III Quadrant IV

Origin (0,0)

CoordinatesRemember, when you give coordinates - or ordered pairs- you must give the x-coordinate and then the y-coordinate.

You write them in parentheses with a comma in the middle.

(x,y) ( , ) (-5,7 )

The Cartesian Plane: Quadrantsy-axis

x-axis

Quadrant I

(+x, +y)

Quadrant II

(-x, +y)

Quadrant III

(-x, -y)

Quadrant IV

(+x, -y)

Let’s Zoom in to the origin.There are countless fractions and decimals between

the whole numbers!

-3 -2 -1 0 1 2 3

3

2

1

0 -1

-2

-3

A ____

B ____

C ____

D ____

E ____

F ____

G ____

H ____

(-3,4)

(0,6)

(6,-3)

(-1,1)

(-4, 0)

(-7, -5)

(2,2)

(0,-5)

10

8

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10E

G

F H

D

C

B

A

Write the coordinates for each point.