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QJEEM21Ma312c: JEE Main 2021 Mathematics - Class 11 JEEM21Ma312c Solution: Let the points of intersections of the lines x y + 1 = 0, x 2y…

Let the points of intersections of the lines x −- y + 1 = 0, x −- 2y + 3 = 0 and 2x −- 5y + 11 = 0 are the mid points of the sides of a triangle Δ\Delta ABC. Then, the area of the Δ\Delta ABC is _____________.

Step-by-Step Verified Solution

Intersection point of given lines are (1, 2), (7, 5), (2, 3)

JEE Main 2021 (Online) 1st September Evening Shift Mathematics - Straight Lines and Pair of Straight Lines Question 66 English Explanation
Δ=12|121751231|

=12[1(5−3)−2(7−2)+1(21−10)]= {1 \over 2}[1(5 - 3) - 2(7 - 2) + 1(21 - 10)]

=12[2−10+11]= {1 \over 2}[2 - 10 + 11]

Δ\Delta DEF =12(3)=32= {1 \over 2}(3) = {3 \over 2}

Δ\Delta ABC = 4 Δ\Delta DEF =4(32)=6= 4\left( {{3 \over 2}} \right) = 6

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