Question

What are the coordinates of point P, that lies `1/5` of the way from `A(-7,-35)` to `B(8, -5)`?

Answer 1

`P=(-4,-29)`

Explanation:

Section formula :
If a point `P(x,y)` divides a line segment joining `A(x_1,y_1) and B(x_2,y_2)` in the ratio `m:n`, i.e., `AP:PB=m:n`,
then `P(x,y)=((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))`
Given `AP:PB=m:n=1/5:4/5=1:4`
`=> P(x,y)=(((1xx8)+(4xx-7))/(1+4)," " ((1xx-5)+(4xx-35))/(1+4))`
`=(-4,-29)`