Question

Find the coordinates of point B along a directed line segment from A(3,4) and

C(3,9) so that the ratio of AB to BC is 4:1.

Answer 1

We have been given two points.
`A(3,4)` and
`C(3,9)`. We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.

We will use segment formula to solve our given problem.

When a point P divides segment any segment internally in the ratio
`m:n`, then coordinates of point P are:

`[\right x=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)\left]`

`(x_1,y_1)=(3,4)` and
`(x_2,y_2)=(3,9)`.

`m=4,n=1`

Upon substituting our given information in above formula, we will get:

`[\right x=(4(3)+1(3))/(4+1),y=(4(9)+1(4))/(4+1)\left]`

`[\right x=(12+3)/(5),y=(36+4)/(5)\left]`

`[\right x=(15)/(5),y=(40)/(5)\left]`

`[\right x=3,y=8\left]`

Therefore, the coordinates of point B would be
`(3,8)`.