Answer:
[tex]P = (\frac{8}{3},\frac{11}{3})[/tex]
Step-by-step explanation:
Given
[tex]X = (1,2)[/tex]
[tex]Y = (6,7)[/tex]
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:
[tex]m:n = 1/3:2/3[/tex]
Multiply by 3
[tex]m:n = 1:2[/tex]
The point (P) is calculated using:
[tex]P = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
This gives:
[tex]P = (\frac{1*6 + 2*1}{1+2},\frac{1*7 + 2*2}{1+2})[/tex]
[tex]P = (\frac{8}{3},\frac{11}{3})[/tex]
