A point P divides the line segment joining A(2, 4) and B(8, 16) internally in the ratio 1 : 2. Find the coordinates of P.
(4, 8)
By the section formula, if P divides A\((x_1, y_1)\) and B\((x_2, y_2)\) internally in the ratio \(m:n\), then \(P = \left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)\).
Here, \(A(2,4)\), \(B(8,16)\), and the ratio is \(1:2\), so \(P = \left(\frac{1(8)+2(2)}{3}, \frac{1(16)+2(4)}{3}\right)\).
This gives \(P = \left(\frac{8+4}{3}, \frac{16+8}{3}\right) = \left(\frac{12}{3}, \frac{24}{3}\right)\).
So the coordinates of P are \((4, 8)\).
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