Question

Given directed line segment qs find the coordinates of r such that the ratio of qr to rs is 3:5 plot point r

Answer 1

Let
`q` and
`s` be the points
`(a,b)` and
`(c,d)` in the coordinate plane. A point on the directed line segment
`qs` can be parameterized by

`(a,b) (1-t) + (c,d) t`

where
`0\le t\le1`.

The point
`r` is 3/8 of the way along this segment, so that its coordinates are

`(a,b) \left(1 - \frac38\right) + (c,d) \frac38 = \left(\frac{5a+3c}8, \frac{5b+3d}8\right)`

Presumably you know more about the
`q` and
`s`, specifically their coordinates. Plug them in to get the numerical coordinates of
`r`.