Question

The ratio in which the point \(\mathrm{P}(1, 2)\) divides the join of the points \(\mathrm{A}(-2, 1)\) and \(\mathrm{B}(7, 4)\) is ______.

Options

• 1 : 2

• 2 : 1

• 3 : 2

• 2 : 3

Answer 1

The ratio in which the point \(\mathrm{P}(1, 2)\) divides the join of the points \(\mathrm{A}(-2, 1)\) and \(\mathrm{B}(7, 4)\) is 1 : 2.

Explanation:

Let the ratio be m : n.

Then \(\frac{4m + 1 \cdot n}{m + n} = 2\)

\(\Rightarrow 2m = n\), so \(m : n = 1 : 2\). 

Check: \(x = \frac{1 \times 7 + 2 \times (-2)}{3} = 1\).