Q42 / 90 · JEE Main 2019 (10 Jan Shift 2) · Mathematics

Two sides of a parallelogram are along the lines, $x + y = 3$ and $x - y + 3 = 0 .$ If its diagonals intersect at $(2, 4),$ then one of its vertex is:

Correct answer
A
$(3, 6)$
B
$(2, 6)$
C
$(2, 1)$
D
$(3, 5)$

Solution

As $B C ∥ A D \Rightarrow {Slope}_{B C} = {Slope}_{A D}$

Hence, slope of $B C = 1 \Rightarrow \frac{3 - h - 5}{h - 4} = 1$

$\Rightarrow - h - 2 = h - 4 \Rightarrow 2 h = 2 \Rightarrow h = 1$

$∴ B (1, 2)$ and $D (3, 6)$

Hence, the correct answer is option: 'A'.

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Two sides of a parallelogram are along the lines, x+y=3 and x-y+3=0. If its diagonals intersect at 2,4, then one of its vertex is:

Solution

Relevant Questions

Two sides of a parallelogram are along the lines, $x + y = 3$ and $x - y + 3 = 0 .$ If its diagonals intersect at $(2, 4),$ then one of its vertex is: