Question

In what ratio does the point (15, 22.5) divide the line joining A(10,20) and B(30,30)?

The ratio is 1 : __

Answer 1

The equation for the point that divides a line in the ratio m:n is,

$(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{n+m})$

Where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the line. Substituting the values in the equation,

(15, 22.5) = $(\frac{10\times n+30\times m}{n+m},\frac{20\times n+30\times m}{n+m})$

15n +15m = 10n +30m
15m = 5n
3m =n
m: n = 1:3
Therefore m: n = 1:3