Question:
The equation of the line passing through the origin and perpendicular to the line joining the points \(A(4,-3)\) and \(B(6,3)\) is
The equation of the line passing through the origin and perpendicular to the line joining the points \(A(4,-3)\) and \(B(6,3)\) is
Show Hint
If the slope of a line is \(m\), then the slope of a line perpendicular to it is
\[
-\frac{1}{m}.
\]
A line through the origin with slope \(m\) is
\[
y=mx.
\]
Updated On: Jul 15, 2026
- \(x+3y=0\)
- \(3x+y=0\)
- \(x-3y=0\)
- \(3x-y=0\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Find the slope of line \(AB\).
\[
m_{AB}
=\frac{3-(-3)}{6-4}
=\frac{6}{2}
=3
\]
Step 2: Find the slope of the required line. Since the required line is perpendicular to \(AB\), \[ m=-\frac{1}{3} \]
Step 3: Equation through the origin. Using point-slope form, \[ y=-\frac13x \] Multiplying by \(3\), \[ x+3y=0 \]
Step 4: Final conclusion. \[ \boxed{x+3y=0} \] Hence, the correct option is \(\boxed{(A)}\).
Step 2: Find the slope of the required line. Since the required line is perpendicular to \(AB\), \[ m=-\frac{1}{3} \]
Step 3: Equation through the origin. Using point-slope form, \[ y=-\frac13x \] Multiplying by \(3\), \[ x+3y=0 \]
Step 4: Final conclusion. \[ \boxed{x+3y=0} \] Hence, the correct option is \(\boxed{(A)}\).
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