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Distance between the lines \( \Large 5x+3y-7=0\ and\ 15x+9y+14=0 \) is:

A) \( \Large \frac{35}{\sqrt{34}} \)
B) \( \Large \frac{1}{\sqrt{34}} \)
C) \( \Large \frac{35}{2\sqrt{34}} \)
D) \( \Large \frac{35}{3\sqrt{34}} \)

Correct Answer:




D) \( \Large \frac{35}{3\sqrt{34}} \)

Description for Correct answer:

Given equation of lines are

\( \Large 5x+3y-7=0 \) ...(i)

and \( \Large 15x+9y+14=0\ or\ 5x+3y+\frac{14}{3}=0 \) ...(ii)

Therefore, Lines (i) and (ii) are parallel and \( \Large C_{1} \) and \( \Large C_{2} \) and of opposite signs, therefore these lines are on opposite sides of the origin, so the distance between them is

\( \Large |\frac{C_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}| + |\frac{C_{2}}{\sqrt{a_{1}^{2}|+b_{2}^{2}}}| = |\frac{7}{\sqrt{5^{2}+3^{2}}}| + |\frac{14}{3\sqrt{5^{2}+3^{2}}}|\) \( \Large = |-\frac{7}{\sqrt{34}}| + |\frac{14}{3\sqrt{34}}| = \frac{35}{3\sqrt{34}} \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines

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