If three vertices of a rhombus taken in order are (2, -1), (3, 4) and (-2, 3), then the fourth vertex is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (-3, -2)
A rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other: the midpoint of AC is the midpoint of BD. Taking the vertices in order as A(2, −1), B(3, 4), C(−2, 3) and D(x, y):
Midpoint of AC: \(\left(\displaystyle\frac{2-2}{2},\ \frac{-1+3}{2}\right)=(0,\ 1)\)
Midpoint of BD: \(\left(\displaystyle\frac{3+x}{2},\ \frac{4+y}{2}\right)\)
\(3+x=0\), so \(x=-3\); \(4+y=2\), so \(y=-2\)