If the points A(3, 0), B(x, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus, taken in order, find the value of x.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
A rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other. So the midpoint of diagonal AC is the same point as the midpoint of diagonal BD.
Midpoint of AC \(\displaystyle =\left(\frac{3+(-1)}{2},\ \frac{0+4}{2}\right)=(1,\ 2)\)
Midpoint of BD \(\displaystyle =\left(\frac{x+(-2)}{2},\ \frac{5+(-1)}{2}\right)=\left(\frac{x-2}{2},\ 2\right)\)
Equating the x-coordinates: \(\displaystyle \frac{x-2}{2}=1\), so \(x=4\)
