LEAVE A COMMENT FOR US

Home > Algebra > Coordinate Geometry > Examples of Division of an Interval

Examples of Division of an Interval

We now look at an examples of division of an interval in a given ratio:

 

Example 1: If A and B are points (1, 2) and (3, 6) respectively, find the coordinates of the point that divides AB in the ratio of 3:2 internally.

A (1, 2) and B (3, 6)

m = 3, and n = 2

x1  =  1,  y1  =  2

x2  =  3,  y2  =  6

x  =  {~mx_2~+~nx_1~}/{m~+~n}

=  {~3~*~3~+~2~*~1~}/{3~+~2}

=  {~9~+~2~}/{5}

=  11/5

y  =  {~my_2~+~ny_1~}/{m~+~n}

=  {~3~*~6~+~2~*~2~}/{3~+~2}

=  {~18~+~4~}/{5}

=  22/5

So the coordinates of the required point are (11/5,~22/5).

 

Example 2: If A and B are the points (1,2) and (3, 6) respectively, and P is the point which divides AB in the ratio of 3:2 externally. Find the coordinates of P.

Here A (1, 2) so x1  =  1,  y1  =  2, and B (3, 6) so x2  =  3,  y2  =  6.

P divides AB externally 3:2 i.e. 3:-2. So m = 3 and n = -2, and P lies outside AB.

x  =  {~mx_2~+~nx_1~}/{m~+~n}

=  {~3~*~3~-~2~*~1~}/{3~-~2}

=  {~9~-~2~}/{1}

=  7

y  =  {~my_2~+~ny_1~}/{m~+~n}

=  {~3~*~6~-~2~*~2~}/{3~-~2}

=  {~18~+~4~}/{1}

=  14

So P (7, 14) is the required point.

 

Learn how to find the perpendicular distance of a point from a line