Question

In the given figure P(5, −3) and Q(3, y) are the points of trisection of the line segment
joining A(7, −2) and B(1, −5). Then, y equals [CBSE 2012]

(a) 2 (b) 4 (c) −4 (d) $\frac{-5}{2}$

Answer 1

Here, AQ : BQ = 2 : 1. Then
$$\begin{gathered} y=\frac{2\times \left(-5\right)+1\times \left(-2\right)}{2+1} \\ =\frac{-10-2}{3} \\ =-4 \end{gathered}$$
Hence, the correct answer is option (c).