NCERT · Class 11 · Mathematics · Straight LinesWhat is the slope of a line perpendicular to the line passing through the points $(1, -2)$ and $(4, 6)$?
Step-by-Step Solution
First, find the slope $m_1$ of the line passing through $(1, -2)$ and $(4, 6)$: $m_1 = \frac{6 - (-2)}{4 - 1} = \frac{8}{3}$. The slope $m_2$ of a line perpendicular to this line satisfies $m_1 \cdot m_2 = -1$. Thus, $m_2 = -\frac{1}{m_1} = -\frac{3}{8}$. Therefore, the correct option is A.
Detailed Options Breakdown
Option : $-\frac{3}{8}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $\frac{8}{3}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.
Option 2: $\frac{3}{8}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.
Option 3: $-\frac{8}{3}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.
💡 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.