JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Straight Lines

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If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is:

(A) $5 x - 3 y + 1 = 0$ ✓ Correct
(B) $5 x + 3 y - 11 = 0$
(C) $3 x - 5 y + 7 = 0$
(D) $3 x + 5 y - 13 = 0$

Answer: (A)

Solution

In the parallelogram ABDC the vertices run A, B, D, C, so the diagonals are AD and BC and they bisect each other. The midpoint of BC, with B

(3, 4)

and C

(2, 5)

, is

(\frac{5}{2}, \frac{9}{2})

, and this is also the midpoint of AD; with A

(1, 2)

that fixes D

= (4, 7)

. The slope of AD is

\frac{7 - 2}{4 - 1} = \frac{5}{3}

, so through A

(1, 2)

the diagonal is

y - 2 = \frac{5}{3} (x - 1)

, i.e.

5 x - 3 y + 1 = 0

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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