COORDINATE GEOMETRY

1
COORDINATE GEOMETRY

• Distance between 2 points
• Mid-point of 2 points

2
Distance between two points.
y
Using Pythagoras Theorem,
B(18,17)
AB2 (18 - 5)2 (17 - 3)2
17
AB2 132 142
17 3 14 units
3
A(5,3)
18 5 13 units
x
5
18
3
Distance between two points.In general,
y
B(x2,y2)
AB2 (y2-y1)2 (x2-x1)2
y2
Hence, the formula for Length of AB or Distance
between A and B is
Length y2 y1
y1
A(x1,y1)
Length x2 x1
x
x1
x2
4
Find the distance between the points (-1,3) and
(2,-6)

• Simply by using the formula

(-1,3) and (2,-6)
(x1,y1) and (x2,y2)
Since
9.49 units (3 sig. fig)
5
The mid-point of two points.
Look at its horizontal length
y
Mid-point of AB
B(18,17)
17
11.5
Look at its vertical length
(11.5,
10)
3
A(5,3)
10
x
5
18
6
The mid-point of two points.
Look at its horizontal length
y
B(18,17)
Mid-point of AB
y2
Look at its vertical length
Formula for mid-point is
y1
A(5,3)
x
x1
x2