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JEE Main 201910 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
10 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2019 · 10 January · Evening Shift · Mathematics · Straight Lines

Two sides of a parallelogram are along the lines, x + y = 3 and x -...

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

Options

  1. A(3,6)\left(3, 6\right)
  2. B(2,6)\left(2, 6\right)
  3. C(2,1)\left(2, 1\right)
  4. D(3,5)\left(3, 5\right)

Correct answer

A. (3,6)\left(3, 6\right)

Step-by-step solution

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

As BC∥AD⇒SlopeBC=SlopeADBC ∥ AD ⇒ {Slope}_{BC} = {Slope}_{AD}

Hence, slope of BC=1⇒3−h−5h−4=1BC = 1 ⇒ \dfrac{3 - h - 5}{h - 4} = 1

⇒−h−2=h−4⇒2h=2⇒h=1⇒ - h - 2 = h - 4 ⇒ 2h = 2 ⇒ h = 1

∴∴B\left(1, 2\right)andandD\left(3, 6\right)

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