1. Internal & External Ratio
Coordinate Geometry:
Internal & External Ratio
Division.
By Mr Porter

2. Student need to learn the 2 formulas!
Division of an Interval AB in a given ratio.
Internal Division of an Interval AB.
Given the points A(x1, y1) and B(x2, y2), the coordinates of the point C(x, y) dividing a given interval AB internally in the ratio m : n is:
External Division of an Interval AB.
Given the points A(x1, y1) and B(x2, y2), the coordinates of the point C(x, y) dividing a given interval AB externally in the ratio m : n is:
Note: the first ratio number multiplies the second point and the second ratio number multiplies the first point.
Student need to learn the 2 formulas!

3. Example 1 : Internal Ratio
Given the points A(1, 3) and B(5, 11), find the coordinates of the point P(x, y) which divides the interval AB internally in the ratio 1 : 3.
Draw a rough diagram.
n = 3 •
A(1, 3)
B(5, 11)
P(x, y)
m = 1
The diagram indicates: 1 < x < 5 and 3 < y < 11.
Data: ratio 1 : 3
m n
points A(1, 3) and B(5, 11)
x1 y1
x2 y2
The point P(x, y) = (2, 5)
Mentally check your answers.

4. Example 2 : External Ratio
Given the points A(1, 3) and B(5, 11), find the coordinates of the point P(x, y) which divides the interval AB externally in the ratio 1 : 3.
Draw a rough diagram. •
A(1, 3)
B(5, 11)
P(x, y)
n = 3
m = 1
The diagram indicates: x < 1 and y < 3.
Data: ratio 1 : 3
m n
points A(1, 3) and B(5, 11)
x1 y1
x2 y2
The point P(x, y) = (-1, -1)
Mentally check your answers.

5. Example 3 : Internal Ratio
Given the points A(-6, 3) and P(4, -2), find the coordinates of the point B(x, y) such that P divides the interval AB internally in the ratio 2 : 3.
Draw a rough diagram.
A(-6, 3) •
B(x, y)
P(4, -2)
m = 2
n = 3
The diagram indicates: x > 4 and y < -2.
Data: ratio 2 : 3
m n
points A(-6, 3) and B(x, y)
x1 y1
x2 y2
The point B(x, y) = (19, -9.5)
Mentally check your answers.

6. Example : External Ratio
Given the points A(-7, 2) and P(3, -23), find the coordinates of the point B(x, y) such that P divides the interval AB externally in the ratio 3 : 2.
Draw a rough diagram.
A(-7, 2) •
•P(3,-23)
B(x, y)
m = 3
n = 2
The diagram indicates: -7 < x < 3 and -23 < y < 2.
Data: ratio 3 : 2
m n
points A(-7, 2) and B(x, y)
x1 y1
x2 y2
The point B(x, y) =
Mentally check your answers.