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1. ⇒ (MHT CET 2023 10th May Evening Shift )

Two sides of a square are along the lines $5 x - 12 y + 39 = 0$ and $5 x - 12 y + 78 = 0$ , then area of the square is

A. 9 sq. units.

B. $\frac{1}{3}$ sq. units.

C. 18 sq. units.

D. 3 sq. units.

Correct answer option is (A)

Given equations of lines are $5 x - 12 y + 39 = 0$ and $5 x - 12 y + 78 = 0$ .

Slope of $5 x - 12 y + 39 = 0$ is $\frac{5}{12}$

Slope of $5 x - 12 y + 78 = 0$ is $\frac{5}{12}$

$∴$ Lines are parallel.

$∴$ Distance between two parallel lines $= | \frac{c_{1} - c_{2}}{\sqrt{a^{2} + b^{2}}} |$

$\begin{aligned} = | \frac{39 - 78}{\sqrt{5^{2} + (- 12)^{2}}} | \\ = 3 units \end{aligned}$

$∴$ Side of the square $= 3$ units

$∴$ Area of square $= 3^{2} = 9$ sq. units

⇒Straight Line