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
(a) 3
(b) 4
(c) 0
(d) $\frac{3}{2}$
Solution:
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
$\frac{1+2}{2}=\frac{-1+x}{2}$
$\Rightarrow x-1=3$
$\Rightarrow x=1+3=4$
Hence, the correct answer is option (b).
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