Find the coordinates of p so that p partitions AB in the ratio 2 to 3 with A(7,2) and B(-8,9.5)

Answer 1

For the point p

the x coordiante is 7 + (2/5)(-15)

the y coordinate is 2 + (2/5)(7.5)

Answer 2

The line AB can be parameterised as

AB(t) = A + Bt = (7,2)*(1-t) + (-8,9.5)*t. where 0 <= t <= 1.

To get the point 2/5 of the way from A to B, we set t = 2/5.

Then, the desired point is AB(2/5) = (7,2)*(3/5)+(-8,9.5)*(2/5) = (21/5 - 16/5,6/5 - 19/5) = (1,-13/5).