\(A(-2,\,1)\), \(B(3,\,2)\) and \(C(5,\,6)\) are three vertices of a parallelogram ABCD, taken in order. What are the coordinates of D?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((0,\,5)\)
The diagonals of a parallelogram bisect each other, so diagonals AC and BD have the same mid-point.
Mid-point of AC: \(\displaystyle \left(\frac{-2+5}{2},\,\frac{1+6}{2}\right)=\left(\frac{3}{2},\,\frac{7}{2}\right)\)
Let \(D=(x,\,y)\). Mid-point of BD: \(\displaystyle \left(\frac{3+x}{2},\,\frac{2+y}{2}\right)\)
\(3+x=3\), so \(x=0\)
\(2+y=7\), so \(y=5\)
So \(D=(0,\,5)\)
