Question

One side of the rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are (– 3, 1) and (1, 1). Then the equations of other side is

(a) 7x – 4y + 25 = 0

(b) 4x + 7y = 11

(c) 7x – 4y – 3 = 0

(d) All of these

Answer 1

The correct option (d) All of these   

Explanation:

side of rectangle lie on 4x + 7y + 5 = 0.                          

other two vertices are (1, 1) and (– 3, 1).                          

also (– 3, 1) satisfies equation of line 4x + 7y + 5 = 0

∴ (– 3, 1) lie on that side of rectangle DC. 

∴ equation of side parallel to DC and passing through (1, 1) is 4x + 7y + λ = 0

∴ λ = – 11

 side AB of rectangle lie on line 4x + 7y – 11 = 0 ......(1)

Also slope of DC = [(– 4)/7]

∴ slope of BC = (7/4)

∴ equation of line with slope (7/4) & passing through (1, 1) is y – 1 = (7/4)(x – 1)

i.e. 4y – 4 = 7x – 7

∴ 7x – 4y – 3 = 0 ....(2)

Now equation of side AD, parallel to 7x – 4y – 3 = 0 & passing through (– 3, 1) is given by

7x – 4y + k = 0

i.e. – 21 – 4 + k = 0

i.e. k = 25

∴ eqn : 7x – 4y + 25 = 0 .....(3)

∴ from (1), (2), (3) answer is d.