How does the section formula work when a point divides a line segment in ratio m:n?

The section formula finds a point P that divides the segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n. The coordinates of P are ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)). Notice that m pairs with the second point and n pairs with the first point, this is the part students mix up. For example, the point dividing A(2, 3) and B(8, 9) in ratio 1:2 is ((1×8 + 2×2)/3, (1×9 + 2×3)/3) = (12/3, 15/3) = (4, 5). The midpoint formula is just this with ratio 1:1, which gives the simple averages. Keep the m-with-second, n-with-first order straight and you will not slip.