Question

Solve im giving 40 points ASAP

Answer 1

A point P on the line segment starting at A and ending at B can be parameterized by

`p(t) = (1-t)(-2,-4) + t (6,1)`

with
`0\le t\le1`.

If AP/PB = 3/2, then point P is 3/5 of the length of AB from A, and 2/5 of the length of AB from B. So the coordinates of P are obtained at
`t=\frac35`, and we find

`p\left(\frac35\right) = \left(1-\frac35\right)(-2,-4) + \frac35 (6,1) = \boxed{\left(\frac{14}5, -1\right)}`