Question

Line segment AB is divided by point P in the ratio of 1:4. Point A is (7,5) and point P is (10,14). What are the coordinates of point B?

Answer 1

Given:

The line segment AB is divided by point P in the ratio of 1:4.

Point A is (7,5) and point P is (10,14).

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

Section formula: If a point divide a line segment in m:n, then the coordinates of that point are

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

The line segment AB is divided by point P in the ratio of 1:4.

Using section formula, we get

`P=\left((1(a)+4(7))/(1+4),(1(b)+4(5))/(1+4)\right)`

`(10,14)=\left((a+28)/(5),(b+20)/(5)\right)`

Comparing the coordinates on both sides, we get

`(a+28)/(5)=10`

`a+28=50`

`a=50-28`

`a=22`

And,

`(b+20)/(5)=14`

`b+20=70`

`b=70-20`

`b=50`

Therefore, the coordinates of point B are (22,50).