JEE MAIN - Mathematics (2021 - 26th February Morning Shift - No. 8)
The intersection of three lines x $$-$$ y = 0, x + 2y = 3 and 2x + y = 6 is a :
Right angled triangle
Equilateral triangle
None of the above
Isosceles triangle
Explanation
The given three lines are x $$-$$ y = 0, x + 2y = 3 and 2x + y = 6 then point of intersection,
lines x $$-$$ y = 0 and x + 2y = 3 is (1, 1)
lines x $$-$$ y = 0 and 2x + y = 6 is (2, 2)
and lines x + 2y = 3 and 2x + y = 0 is (3, 0)
The triangle ABC has vertices A(1, 1), B(2, 2) and C(3, 0)
$$ \therefore $$ AB = $$\sqrt 2 $$, BC = $$\sqrt 5 $$ and AC = $$\sqrt 5 $$
$$ \therefore $$ $$\Delta$$ABC is isosceles
lines x $$-$$ y = 0 and x + 2y = 3 is (1, 1)
lines x $$-$$ y = 0 and 2x + y = 6 is (2, 2)
and lines x + 2y = 3 and 2x + y = 0 is (3, 0)
The triangle ABC has vertices A(1, 1), B(2, 2) and C(3, 0)
$$ \therefore $$ AB = $$\sqrt 2 $$, BC = $$\sqrt 5 $$ and AC = $$\sqrt 5 $$
$$ \therefore $$ $$\Delta$$ABC is isosceles
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