Question

Find the coordinates of the point that divides the join of A(−1, 7) and B(4, −3) in the ratio 2 : 3.

Answer 1

The end points of AB are A(−1, 7) and B(4, −3).
Therefore, (x₁ = −1, y₁ = 7) and (x₂ = 4, y₂ = −3)
Also, m = 2 and n = 3
Let the required point be P(x, y).
By section formula, we get:
$$\begin{gathered} x=\frac{\left(m{x}_2+n{x}_1\right)}{\left(m+n\right)},y=\frac{\left(m{y}_2+n{y}_1\right)}{\left(m+n\right)} \\ \Rightarrow x=\frac{\left\{2\times 4+3\times \left(-1\right)\right\}}{2+3},y=\frac{\left\{2\times \left(-3\right)+3\times 7\right\}}{2+3} \\ \Rightarrow x=\frac{8-3}{5},y=\frac{-6+21}{5} \\ \Rightarrow x=\frac{5}{5},y=\frac{15}{5} \\ \mathrm{Therefore},x=1\mathrm{and}y=3 \end{gathered}$$
Hence, the coordinates of the required point are (1, 3).