Section describes the coordinate plane and expands the formulas of 2.1-2.3 into two deminsion

1. Moving into two dimensions

2. 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

3. Special Lines
 x=5  y=6
 A vertical line,  A horizontal line,
perpendicular to the x- perpendicular to the y-
axis y axis y
y=6
x=5
x x

4. 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

5. 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: A B
C
AB + BC = AC
 Midpoint A(Xa, Ya) to B (Xb, Yb)
(XM, YM) = (Xa + Xb) , (Ya + Yb)
2 2