Here, given points are A (-4, 3) and B ( 2, 8) and let the point dividing the line joining two points be P(m,6).
Let the ratio be m:n
By section formula,
x = \(\frac{mx_2+nx_1}{m+n}\), y = \(\frac{my_2+ny_1}{m+n}\)
For point P(m,6),
m = \(\frac{m\times2+n\times(-4)}{m+n}\) …..(1)
And 6 = \(\frac{m\times8+n\times3}{m+n}\)…..(2)
Solving 2 for finding ratio between m and n,
6 = \(\frac{m\times8+n\times3}{m+n}\)
6(m + n) = 8m +3n
6m + 6n = 8m +3n
∴ 2m = 3n
∴ \(\frac{m}n\) = \(\frac{3}2\)
∴ m : n = 3 : 2
Now solving for equation 1, where m = 3 and n =2
m = \(\frac{m\times2+n\times(-4)}{m+n}\)
∴ m = \(\frac{6-8}5\)
∴ m = \(\frac{-2}5\)
Hence, our point is (\(\frac{-2}5\),6)