Introduction to Finding Pythagoras Graphing with Coordinates on the Cartesian Plane

Ancient Math Geek, Rene Descartes took 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 Descartes then 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. 4 3 2 1 -1 -2 -3 -4 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

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

The Cartesian Plane: origin y-axis Quadrant II Quadrant I Origin (0,0) x-axis Quadrant III Quadrant IV

You must walk before you can fly. Coordinates Remember, 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. You must walk before you can fly. ( , ) (-5,7 ) (x,y)

The Cartesian Plane: Quadrants y-axis Quadrant II (-x, +y) Quadrant I (+x, +y) x-axis Quadrant III (-x, -y) Quadrant IV (+x, -y)

Let’s Zoom in to the origin 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

Write the coordinates for each point. (-3,4) A ____ B ____ C ____ D ____ E ____ F ____ G ____ H ____ (0,6) (6,-3) (-1,1) (-4, 0) (-7, -5) (2,2) (0,-5)