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:

The given points A(11, y), B(13, 5), C(14, 7), D(12, 6) are vertices of a parallelogram taken in order.

In any parallelogram, the diagonals bisect each other. This means the midpoint of diagonal AC equals the midpoint of diagonal BD.

Since vertices are taken in order A → B → C → D:

• Diagonal AC connects A to C
• Diagonal BD connects B to D

For diagonal BD with B(13, 5) and D(12, 6):

Midpoint of BD $= \left(\dfrac{13+12}{2}, \dfrac{5+6}{2}\right)$

$= \left(\dfrac{25}{2}, \dfrac{11}{2}\right)$

For diagonal AC with A(11, y) and C(14, 7):

Midpoint of AC $= \left(\dfrac{11+14}{2}, \dfrac{y+7}{2}\right)$

$= \left(\dfrac{25}{2}, \dfrac{y+7}{2}\right)$

Since the diagonals bisect each other, the midpoints are equal:

$\left(\dfrac{25}{2}, \dfrac{y+7}{2}\right) = \left(\dfrac{25}{2}, \dfrac{11}{2}\right)$

The x-coordinates are already equal. Equating the y-coordinates:

$\dfrac{y+7}{2} = \dfrac{11}{2}$

$y + 7 = 11$

$y = 4$

Therefore, the value of y is 4.