Question

Vertices of a quadrilateral ABCD are A (1, 2), B (4, 6),

C (8, 9) and D (5, 5). Then quadrilateral ABCD is

• A. Rhombus
• B. Rectangle
• C. Square
• D. None

Answer 1

Answer: (A)

Rhombus

Answer 2

Mid point of

AC = $\left( \frac{1 + 8}{2},\frac{2 + 9}{2} \right) \Rightarrow \left( \frac{9}{2},\frac{11}{2} \right)$

Mid point BD =

$\left( \frac{4 + 5}{2},\frac{6 + 5}{2} \right) \Rightarrow \left( \frac{9}{2},\frac{11}{2} \right)$

AC =$\sqrt{49 + 49} = 7\sqrt{2}$,BD =$\sqrt{2}$

m₁ = slope of AC = 1

m₂ = slope of BD = –1

m₁m₂ = – 1 q = 90⁰

hence quadrilareral ABCD is Rhombus