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.

4

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:

$\frac{y+7}{2} = 5.5$

$y + 7 = 11$

$y = 4$