JEE MAIN - Mathematics (2021 - 1st September Evening Shift - No. 18)
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 $$\Delta $$ABC. Then, the area of the $$\Delta $$ABC is _____________.
Answer
6
Explanation
Intersection point of given lines are (1, 2), (7, 5), (2, 3)
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$$\Delta = {1 \over 2}\left| {\matrix{ 1 & 2 & 1 \cr 7 & 5 & 1 \cr 2 & 3 & 1 \cr } } \right|$$
$$ = {1 \over 2}[1(5 - 3) - 2(7 - 2) + 1(21 - 10)]$$
$$ = {1 \over 2}[2 - 10 + 11]$$
$$\Delta$$DEF $$ = {1 \over 2}(3) = {3 \over 2}$$
$$\Delta$$ABC = 4$$\Delta$$DEF $$ = 4\left( {{3 \over 2}} \right) = 6$$
$$\Delta = {1 \over 2}\left| {\matrix{ 1 & 2 & 1 \cr 7 & 5 & 1 \cr 2 & 3 & 1 \cr } } \right|$$
$$ = {1 \over 2}[1(5 - 3) - 2(7 - 2) + 1(21 - 10)]$$
$$ = {1 \over 2}[2 - 10 + 11]$$
$$\Delta$$DEF $$ = {1 \over 2}(3) = {3 \over 2}$$
$$\Delta$$ABC = 4$$\Delta$$DEF $$ = 4\left( {{3 \over 2}} \right) = 6$$
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