If A(2, 3), B(2, 4), C(4, 9) and D(\(x\), 8) are the vertices of a parallelogram ABCD, then find the value of \(x\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4
The diagonals of a parallelogram bisect each other, so the midpoint of diagonal AC is also the midpoint of diagonal BD.
Midpoint of AC: \(\displaystyle\left(\frac{2+4}{2},\frac{3+9}{2}\right)=(3,6)\)
Midpoint of BD: \(\displaystyle\left(\frac{2+x}{2},\frac{4+8}{2}\right)=\left(\frac{2+x}{2},6\right)\)
\(\displaystyle\frac{2+x}{2}=3\), so \(x=4\)
