Q84 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

If $\mathrm{A}(-3,3), \mathrm{B}(1,1), \mathrm{C}(1,-1)$ and $\mathrm{D}(-2,-2)$ are the vertices of a quadrilateral, the angle between the diagonals $\mathrm{AC}$ and $\mathrm{BD}$ is

A
$\frac{\pi}{4}$
Correct answer
B
$\frac{\pi}{2}$
C
$\frac{\pi}{6}$
D
$\frac{\pi}{3}$

Solution

$\begin{aligned} & m_{A C}=\frac{-1-3}{1-(-3)}=-1 \\ & m_{B D}=\frac{-2-1}{-2-1}=1 \\ & m_{A C} \times m_{B D}=-1 \times 1=-1\end{aligned}$ $A C$ and $B D$ are perpendicular Angle between $A C$ and $B D=\pi / 2$

Hence, the correct answer is option: 'B'.

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