First slide

Equation of line in Straight lines

Question

The lines x + 2y + 3 = 0, x + 2y - 7 = 0, and 2x - y - 4= 0 are the sides of a square. The equation of the remaining side of the square can be

Moderate

A

2x-y+6=0
B

2x-y+8=0
C

2x-y-10=0
D

2x-y-14=0

Solution

Distance between .x + 2y + 3 = 0 and x + 2y -7 =0 is $10 / \sqrt{5}$ .
Let the remaining side parallel to 2x - y - 4 =0 be $2 x - y + λ = 0$ . We have
$\frac{| λ + 4 |}{\sqrt{5}} = \frac{10}{\sqrt{5}} or λ = 6, - 14$
Thus, the remaining side is2x - y + 6=0 or 2x - y - 14=0.

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