Question

In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.

 P(–2, –5), Q(4, 3), a : b = 3 : 4

Answer 1

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

 P(–2, –5), Q(4, 3), a : b = 3 : 4
Using section formula

\[x = \frac{3 \times 4 + 4 \times \left( - 2 \right)}{3 + 4} = \frac{12 - 8}{7} = \frac{4}{7}\]

\[y = \frac{3 \times 3 + 4 \times \left( - 5 \right)}{3 + 4} = \frac{9 - 20}{7} = \frac{- 11}{7}\]

\[\left( x, y \right) = \left( \frac{4}{7}, \frac{- 11}{7} \right)\]