If the points P(8, 5), Q(4, 8), R(0, 5) and S(4, k) are the vertices of a rhombus, taken in order, then the value of k is

2

The correct answer is Option (4) → 2

In a rhombus, the diagonals bisect each other.

• Midpoint of PR where P(8, 5) and R(0, 5):

$\left(\frac{8+0}{2}, \frac{5+5}{2}\right) = (4, 5)$

• Midpoint of QS where Q(4, 8) and S(4, k):

$\left(\frac{4+4}{2}, \frac{8+k}{2}\right) = (4, \frac{8+k}{2})$

Equating the y-coordinates of the midpoints:

$\frac{8+k}{2} = 5 \Rightarrow 8+k = 10 \Rightarrow k = 2$