Question

If the four vertices of a rhombus taken in order are (0, 0), (a, –3), (7, b) and (3, 4), then (b, a) is equal to

• A.
  $(6,3)$
• B.
  $(1,3)$
• C.
  $(-3,4)$
• D.
  $(1,4)$

Answer 1

The correct option is D

$(1,4)$
Let the rhombus be ABCD.

Therefore, the vertices in order are A(0, 0), B( a, –3), C(7, b) and D(3, 4).

Since, the diagonals of a rhombus bisects each other.

$\therefore$ Mid-point of AC = Mid-point of BD

$\Rightarrow (\frac{0+7}{2},\frac{0+b}{2})=(\frac{a+3}{2},\frac{-3+4}{2})\Rightarrow (\frac{7}{2},\frac{b}{2})=(\frac{a+3}{2},\frac{1}{2})\Rightarrow \frac{7}{2}=\frac{a+3}{2}and\frac{b}{2}=\frac{1}{2}\Rightarrow a=4andb=1\therefore (b,a)=(1,4)$

Hence, the correct answer is option (d).