Question

What are the coordinates of point P on a directed line segment from R to Q such that P is 5/6 the length of the line segment.

Answer 1

`P = [-3/5,2.33]`

Explanation:

Given

See attachment for line segment RQ

`P = (5)/(6)` of RQ

Required

The coordinates of P

Using line segment ratio formula, we have:

`P = [(mx_2 + nx_1)/(m+n),(my_2 + ny_1)/(m+n)]`

If P is at:

`P = (5)/(6)`

Then:

`m : n = (5)/(6) : 1 -(5)/(6)`

Solve

`m : n = (5)/(6) : (6-5)/(6)`

`m : n = (5)/(6) : (1)/(6)`

Multiply by 6

`m : n = (5)/(6) *6: (1)/(6) * 6`

`m : n = 5 : 1`

By comparison

`m=5\ \& n = 1`

From the attached line segment

`R(x_1,y_1) = (4,-1)`

`Q(x_2,y_2) = (-5,3)`

So, we have:

`P = [(5*-5 + 1*4)/(5+1),(5*3 + 1*-1)/(5+1)]`

`P = [(-25 + 4)/(6),(15 -1)/(6)]`

`P = [(-21)/(6),(14)/(6)]`

`P = [-3/5,2.33]`