Question

In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–3, 7), Q(1, –4), a : b = 2 : 1

Answer 1

Let the coordinates of point A be (x, y).

 P(–3, 7), Q(1, –4), a : b = 2 : 1
Using section formula

\[x = \frac{2 \times 1 + 1 \times \left( - 3 \right)}{2 + 1} = \frac{2 - 3}{3} = \frac{- 1}{3}\]

\[y = \frac{2 \times \left( - 4 \right) + 1 \times 7}{2 + 1} = \frac{- 8 + 7}{3} = \frac{- 1}{3}\]

\[\left( x, y \right) = \left( \frac{- 1}{3}, \frac{- 1}{3} \right)\]