Question:
The equation of line passing through \((-3,5)\) and perpendicular to the line through the points \((2,5)\) and \((-3,6)\) is:
The equation of line passing through \((-3,5)\) and perpendicular to the line through the points \((2,5)\) and \((-3,6)\) is:
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For perpendicular lines, slopes satisfy \(m_1m_2=-1\).
Updated On: May 19, 2026
- \(5x+y-20=0\)
- \(5x-y+20=0\)
- \(5x-2y+40=0\)
- \(5x+2y-40=0\)
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The Correct Option is B
Solution and Explanation
Concept:
If two lines are perpendicular, then: \[ m_1m_2=-1 \]
Step 1: Find slope of line through \((2,5)\) and \((-3,6)\). \[ m_1=\frac{6-5}{-3-2} \] \[ m_1=\frac{1}{-5} \] \[ m_1=-\frac{1}{5} \]
Step 2: Find slope of perpendicular line. \[ m_1m_2=-1 \] \[ -\frac{1}{5}m_2=-1 \] \[ m_2=5 \]
Step 3: Use point-slope form.
Line passes through \((-3,5)\), so: \[ y-5=5(x+3) \] \[ y-5=5x+15 \] \[ y=5x+20 \] \[ 5x-y+20=0 \] \[ \therefore \text{Correct Answer is (B)} \]
If two lines are perpendicular, then: \[ m_1m_2=-1 \]
Step 1: Find slope of line through \((2,5)\) and \((-3,6)\). \[ m_1=\frac{6-5}{-3-2} \] \[ m_1=\frac{1}{-5} \] \[ m_1=-\frac{1}{5} \]
Step 2: Find slope of perpendicular line. \[ m_1m_2=-1 \] \[ -\frac{1}{5}m_2=-1 \] \[ m_2=5 \]
Step 3: Use point-slope form.
Line passes through \((-3,5)\), so: \[ y-5=5(x+3) \] \[ y-5=5x+15 \] \[ y=5x+20 \] \[ 5x-y+20=0 \] \[ \therefore \text{Correct Answer is (B)} \]
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