If point P divides segment AB in the ratio 1 : 3 where A(–5, 3) and B(3, –5), then the coordinates of P are ______.

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If point P divides segment AB in the ratio 1 : 3 where A(–5, 3) and B(3, –5), then the coordinates of P are (–3, 1). Explanation: Let A(x1, y1) = A(–5, 3) and B(x2, y2) = B(3, –5), a : b = 1 : 3 $\therefore$ x1 = –5, y1 = 3, x2 = 3, y2 = –5, a = 1, b = 3 $\therefore$ By section formula, x = (ax_2 + bx_1)/(a + b) = (1(3) + 3(-5))/(1 + 3) = (3 - 15)/(4) = (- 12)/(4) $\therefore$ x = –3 y = (ay_2 + by_1)/(a + b) = (1(-5) + 3(3))/(1 + 3) = (-5 + 9)/(4) = (4)/(4) $\therefore$ y = 1 $\therefore$ Co-ordinates of P are (–3, 1).

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