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JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2025 · 2 April · Evening Shift · Mathematics · Straight Lines

Let A(4,-2), B(1,1) and C(9,-3) be the vertices of a triangle A B C...

Let A(4,−2),B(1,1)\mathrm{A}(4,-2), \mathrm{B}(1,1) and C(9,−3)\mathrm{C}(9,-3) be the vertices of a triangle ABCA B C. Then the maximum area of the parallelogram AFDE , formed with vertices D,E\mathrm{D}, \mathrm{E} and F on the sides BC,CA\mathrm{BC}, \mathrm{CA} and AB of the triangle ABC respectively, is ______ .

Correct answer

0

Step-by-step solution

Area of \triangle \mathrm{ABC}=\frac{1}{2}\left|4−211119−31\begin{array}{ccc}4 & -2 & 1 \\ 1 & 1 & 1 \\ 9 & -3 & 1\end{array}\right|
=6=6 square units
Maximum area of AFDE⁡=12×6=3\operatorname{AFDE}=\frac{1}{2} \times 6=3 sq. units
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