Question

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

Options

• \((4, -7)\)

• \(\left(\frac{7}{2}, 4\right)\)

• \((8, 4)\)

• \((12, 8)\)

Answer 1

The coordinates of the point P which divides the join of A(5, –2) and B(9, 6) in the ratio 3 : 1 are (8, 4).

Explanation:

Using the section formula with \(m = 3, n = 1\): 

$$x = \frac{3 \times 9 + 1 \times 5}{4}$$

$$= \frac{32}{4}$$

$$= 8$$ 

$$y = \frac{3 \times 6 + 1 \times (-2)}{4}$$

$$= \frac{16}{4}$$

$$= 4$$ 

Hence P(8, 4).