Question

A(-3, -2) and B(6, 1), determine the coordinates of point P on directed line segment stack A B with bar on top that partitions stack A B with bar on top in a ratio of 2:1

Answer 1

P(3,0)

Explanation:

We want to find the coordinates of P(x,y), that partitions
`\overline{AB}` in the ration m:n=2:1.

where
`(x_1,y_1)=A(-3,-2)` and
`(x_2,y_2)=B(6,1)`.

This is given by:

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

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

We substitute the values to get:

`x=(2*6+1*-3)/(2+1)`

`x=(9)/(3)=3`

`y=(2*1+1*-2)/(2+1)`

`y=(2-2)/(2+1)`

`y=(0)/(3)=0`

The coordinates are (3,0)