Question

Find the point B on Line AC such that the ratio of AB to BC is 3:4

Answer 1

The point B will be at (5,1)

Explanation:

In order to solve this we just have to calculate both components, so in the component x and y, in x the change in units is 7, and in the component y the change is 14.

Since the change is 3:4 AB will be 3x and BC will be 4x

3x+4x=7

7x=7

x=1

3x+4x=14

7x=14

x=2

AB in x measures 3 and in y measures 6.

While BC in x measures 4 and in Y measures 8.

So the point should be at Ax-3 and Ay+6

Ax-3 Ay+6

8-3=5 -5+6=1

The point B will be at (5,1)

Answer 2

`B(5,1)`

Explanation:

The coordinates of A are (8,-5) and that of C are (1,9).

We want to find the coordinates of B(x,y) that divides
`\overline{AC}`.

in the ratio m:n=3:4

This is given by:

`x=(mx_2+nx_1)/(m+n)`

and

`y=(my_2+ny_1)/(m+n)`

We substitute the points and m=3,n=4 to get.

`x=(3*1+4*8)/(3+4)`

`x=(3+32)/(7)`

`x=(35)/(7)=5`

`y=(3*9+4*-5)/(3+4)`

`y=(27-20)/(3+4)`

`y=(7)/(7)=1`

The coordinates are
`(5,1)`