Question

For the line segment whose endpoints are X (1, 2) and Y (6, 7), find the x coordinate for the point located 1 over 3 the distance from X to Y.

Answer 1

`P = ((8)/(3),(11)/(3))`

Explanation:

Given

`X = (1,2)`

`Y = (6,7)`

Required

The point at 1/3 of XY

If the point is at 1/3 for X, then the other end (to Y) is 2/3

So, we have:

`m:n = 1/3:2/3`

Multiply by 3

`m:n = 1:2`

The point (P) is calculated using:

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

This gives:

`P = ((1*6 + 2*1)/(1+2),(1*7 + 2*2)/(1+2))`

`P = ((8)/(3),(11)/(3))`