Finding the point that divides a line segment according to a given ratio. (the proof for the formula)....?

Question

E is a point that divides the line segment A(x1, y1) and B(x2,y2) internally in the ratio AE:EB = m:n.

The coordinates of the point E =
((nx1+mx2)/(m+n) , (ny1+my2)/(m+n))

Would you show me the proof or tell me where can I find one?

Answer 1

(Ex - x1) / (x2 - x1) = m / (m + n)
(Ey - y1) / (y2 - y1) = m/(m + n)
(Ex - x1) (m + n) = m (x2 - x1)
Ex(m + n) - mx1 - nx1 = mx2 - mx1
Ex(m + n) = mx2 - mx1 + mx1 + nx1
Ex(m + n) = mx2 + nx1
Ex = (nx1 + mx2) / (m + n)
Ey follows exactly the same form, so
Ey = (ny1 + my2) / (m + n)
Combining,
E = ((nx1 + mx2) / (m + n), (ny1 + my2) / (m + n))