Question

A point P divides the join of A(5, −2) and B(9, 6) in the ratio 3 : 1. The coordinates of P are

(a) (4, 7)
(b) (8, 4)
(c) (12, 8)
(d) $\left(\frac{11}{2},5\right)$

Answer 1

(b) (8, 4)
The given points are A(5, −2) and B(9, 6)
Then, $\left(x_1=5,y_1=-2\right)\text{and}\left(x_2=9,y_2=6\right)$
Also, m ​= 3 and n = 1
Let the required point be P(x, y).
By section formula, we have
$$\begin{gathered} x=\frac{m{x}_2+n{x}_1}{m+n},y=\frac{m{y}_2+n{y}_1}{m+n} \\ \Rightarrow x=\frac{\left(3\times 9+1\times 5\right)}{\left(3+1\right)},y=\frac{\left(3\times 6+1\times \left(-2\right)\right)}{\left(3+1\right)} \\ \Rightarrow x=\frac{32}{4},y=\frac{16}{4} \\ \Rightarrow x=8,y=4 \end{gathered}$$
Hence, the coordinates of P are (8, 4).