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
In a parallelogram, the diagonals bisect each other.
So, the midpoint of diagonal AC equals the midpoint of diagonal BD.
Given points:
- A(11, y)
- B(13, 5)
- C(14, 7)
- D(12, 6)
Midpoint of AC
$\left(\frac{11+14}{2},\; \frac{y+7}{2}\right) = \left(12.5,\; \frac{y+7}{2}\right)$
Midpoint of BD
$\left(\frac{13+12}{2},\; \frac{5+6}{2}\right) = (12.5,\; 5.5)$
Equating the y-coordinates:
$\frac{y+7}{2} = 5.5$
$y + 7 = 11$
$y = 4$