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Question

# Consider a parallelogram whose sides are represented by the lines 2x+3y=0;2x+3y−5=0 , 3x−4y=0 and 3x−4y=3. The equation of the diagonal not passing through the origin, is

A
21x11y+15=0
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B
9x11y+15=0
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C
21x29y15=0
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D
21x11y15=0
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Solution

## The correct option is D 21x−11y−15=0Let AB⇒2x+3y=0BC⇒3x−4y=0CD⇒2x+3y−5=0AD⇒3x−4y=3And considering B to be origin So, A≡ solution of AB and ADso, A≡(917,−617)and C≡ solution of BC and CDso, C≡(2017,1517)So, Equation of AC will be a follows :-(y−1517)=⎛⎜ ⎜ ⎜ ⎜⎝1517−(−617)2017−917⎞⎟ ⎟ ⎟ ⎟⎠×(x−2017)i.e, 21x−11y−15=0Hence, this is the answer.

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