Question

If A(1, 3), B(−1, 2) and C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is [CBSE 2012]
(a) 3 (b) 4 (c) 0 (d) $\frac{3}{2}$

Answer 1

The diagonals of a parallelogram bisect each other. The vertices of the ||gm ABCD are A(1, 3), B(−1, 2) and C(2, 5) and D(x, 4).
Here, AC and BD are the diagonals. So
$$\begin{gathered} \frac{1+2}{2}=\frac{-1+x}{2} \\ \Rightarrow x-1=3 \\ \Rightarrow x=1+3=4 \end{gathered}$$
Hence, the correct answer is option (b).