Moving into two dimensions

The Coordinate Plane Ordered pairs (X,Y) A convention to make it

easy

X-axis marks left and right Right is positive

Left is negative

y-axis goes up and down Up is positive

Down is negative

To plot, Count over X units, then

Count up/down for Y

Note the quadrants (I to

Special Lines

x = 5

A vertical line,

perpendicular to the x-

axis

y = 6

A horizontal line,

perpendicular to the y-

axis

x

y

x

y

y = 6x = 5

Segments on the Coordinate

Plane

Like in 1 dimension, any two points can define a

segment

Segments have a defined length

Segments can be added.

A segment’s midpoint is found by finding the

midpoint for both X and Y

Segment Formulas Length (distance) A(Xa, Ya) to B (Xb, Yb)

d = AB = √ (Xb - Xa)2 + (Yb - Ya)2

Note this looks different than the 1-d formula, but it is

equivalent

Segment addition:

AB + BC = AC

Midpoint A(Xa, Ya) to B (Xb, Yb)

(XM, YM) = (Xa + Xb) , (Ya + Yb)

2 2

A B

C