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NCERT · Class 11 · Mathematics · Straight LinesWhat is the distance between the parallel lines $3x - 4y + 7 = 0$ and $3x - 4y + 5 = 0$?

Q: What is the distance between the parallel lines $3x - 4y + 7 = 0$ and $3x - 4y + 5 = 0$?

The distance $d$ between two parallel lines $Ax + By + C1 = 0$ and $Ax + By + C2 = 0$ is given by $d = \frac{|C1 - C2|}{\sqrt{A^2 + B^2}}$. Here $A = 3, B = -4, C1 = 7, C2 = 5$. Substituting the values: $d = \frac{|7 - 5|}{\sqrt{3^2 + (-4)^2}} = \frac{2}{\sqrt{9 + 16}} = \frac{2}{\sqrt{25}} = \frac{2}{5}$. Therefore, the correct option is D.

Step-by-Step Solution

The distance $d$ between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$. Here $A = 3, B = -4, C_1 = 7, C_2 = 5$. Substituting the values: $d = \frac{|7 - 5|}{\sqrt{3^2 + (-4)^2}} = \frac{2}{\sqrt{9 + 16}} = \frac{2}{\sqrt{25}} = \frac{2}{5}$. Therefore, the correct option is D.

Detailed Options Breakdown

Option : $12/5$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

Option 1: $1/5$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

Option 2: $7/5$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

Option 3: $2/5$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

💡 Study Guide: This question tests core syllabus concepts from Straight Lines. For formulas, key summaries, and mock exam reference guides, read the full Straight Lines Revision Notes.

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