Question

In the adjoining figure, \(\mathrm{P}(5, -3)\) and \(\mathrm{Q}(3, y)\) are the points of trisection of the line segment joining \(\mathrm{A}(7, -2)\) and \(\mathrm{B}(1, -5)\). Then, y equals:  

Options

• – 4

• \(-\frac{5}{2}\)

• 2

• 4

Answer 1

– 4

Explanation:

Q is the second point of trisection, so it divides AB in the ratio 2 : 1:

$$x = \frac{2 \times 1 + 1 \times 7}{3} = 3$$

$$y = \frac{2 \times (-5) + 1 \times (-2)}{3} = -4$$

Hence y = – 4.