Question

Find the coordinates of point P if P divides the line segment joining the points A(–1,7) and B(4,–3) in the ratio 2 : 3.

Answer 1

Let the coordinates of point P be (x, y).
The ratio in which P divides A(–1,7) and B(4,–3) is 2 : 3.
Using the section formula we have
$$\begin{gathered} x=\frac{4\times 2+3\times \left(-1\right)}{2+3}=\frac{8-3}{5}=1 \\ y=\frac{2\times \left(-3\right)+3\times 7}{2+3}=\frac{-6+21}{5}=3 \end{gathered}$$
Thus, the coordinates of point P are (1, 3).