AP EAMCET · Maths · Straight Lines
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 \(\frac{\pi}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & m_{A C}=\frac{-1-3}{1-(-3)}=-1 \\ & m_{B D}=\frac{-2-1}{-2-1}=1 \\ & m_{A C} \times m_{B D}=-1 \times 1=-1\end{aligned}\) \(A C\) and \(B D\) are perpendicular Angle between \(A C\) and \(B D=\pi / 2\)
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