Find a point P which divides internally the line segment joining the points A(-3, 9) and B(1, -3) in the ratio 1 : 3.

Let Point P divides the line segment joining A(−3, 9) and B(1, −3) internally in the ratio m₁ : m₂ = 1 : 3.

By using section formula,

P(x, y) = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values we get:

$P = \Big(\dfrac{1 \times 1 + 3 \times -3}{1 + 3}, \dfrac{1 \times -3 + 3 \times 9}{1 + 3}\Big) \\[1em] = \Big(\dfrac{1 - 9}{4}, \dfrac{-3 + 27}{4}\Big) \\[1em] = \Big(\dfrac{-8}{4}, \dfrac{24}{4}\Big) \\[1em] = (-2, 6).$

Hence, coordinates of P = (-2, 6).