
LESSON 1 : COORDINATE GEOMETRY
Consider the grid
below. The center of the grid is called
the origin (Point O). The horizontal number line is called the
xaxis.
The vertical number line is
called the yaxis. Any point in the xy plane may be located with
reference to the origin using two numbers,
called an ordered pair of numbers (x,y). Complete the chart and graph below (Example
1)to see how this is done.
Example 1:
POINT 
LOCATION FROM ORIGIN IN WORDS 
ORDERED PAIR (x,y) 
A 
right 1, up 2 
A(1,2) 
B 
left 3, up 4 
B(3,4) 
C 
right 5, down 2 
C(5,2) 
D 

D( , ) 
E 

E( , ) 
F 

F( , ) 
G 

G( , ) 
H 

H( , ) 
I 

I( , ) 
J 

J( , ) 
K 

K( , ) 
L 

L( , ) 
Solution:
POINT 
LOCATION FROM ORIGIN IN WORDS 
ORDERED PAIR (x,y) 
A 
right 1, up 2 
A(1, 2) 
B 
left 3, up 4 
B(3, 4) 
C 
right 5, down 2 
C(5, 2) 
D 
left 2 down 4 
D(2, 4) 
E 
right 1, down 3 
E(1, 3) 
F 
left 5, down 5 
F(5, 5) 
G 
right 6 up 1 
G(6, 1) 
H 
left 5, up 7 
H(5, 7) 
I 
right 4, no up 0 
I(4, 0) 
J 
left 6, up 0 
J( 6, 0) 
K 
right 0, up 3 
K(0, 3) 
L 
right 0, down 1 
L(0,1) 
The elements of column 3 are
called ordered pairs. Each ordered pair has an xcoordinate and a
ycoordinate (x , y).
The horizontal number line
is called the xaxis.
The vertical number line is the yaxis. The
origin has coordinates (0 , 0).
Example 2:
Sketch
and describe the regions given by the following set descriptions.
a) This region is all the points in the plane on the vertical line x = 2 or to the right of it. See graph below
b) This region is all the points in the plane on the horizontal line y = 3 or below it. See graph below
c) This region is all the points in the plane to the right of the line x = 1, but not including the line, and to the left of the line x = 2, including the
points on the line. The line x = 1 is dashed to show the points on the line are not included.
a)
Distance Between Two Points (length of a
line segment)