If A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram ABCD, then find the values of x and y.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x=6, y=3\)
The diagonals of a parallelogram bisect each other, so the diagonals AC and BD have the same midpoint.
Midpoint of AC \(\displaystyle =\left(\frac{1+x}{2},\ \frac{2+6}{2}\right)\)
Midpoint of BD \(\displaystyle =\left(\frac{4+3}{2},\ \frac{y+5}{2}\right)\)
x-coordinates: \(1+x=7\), so \(x=6\)
y-coordinates: \(8=y+5\), so \(y=3\)
