If the points A(11, y), B(13, 5), C(14, 7) and D(12, 6) are the vertices of a parallelogram, taken in order, find the value of y.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
The diagonals of a parallelogram bisect each other, so the diagonals AC and BD (vertices taken in order) have the same midpoint.
Midpoint of BD \(\displaystyle =\left(\frac{13+12}{2},\ \frac{5+6}{2}\right)=\left(\frac{25}{2},\ \frac{11}{2}\right)\)
Midpoint of AC \(\displaystyle =\left(\frac{11+14}{2},\ \frac{y+7}{2}\right)=\left(\frac{25}{2},\ \frac{y+7}{2}\right)\)
Equal \(y\)-coordinates: \(y+7=11\), so \(y=4\)