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
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
The diagonals of a rhombus bisect each other (as in every parallelogram). With the vertices taken in order, the diagonals are PR and QS, so the midpoint of PR is also the midpoint of QS.
Midpoint of PR \(\displaystyle =\left(\frac{8+0}{2},\frac{5+5}{2}\right)=(4,5)\)
Midpoint of QS \(\displaystyle =\left(\frac{4+4}{2},\frac{8+k}{2}\right)=\left(4,\frac{8+k}{2}\right)\)
\(\displaystyle\frac{8+k}{2}=5\), so \(8+k=10\) and \(k=2\)
