Question

If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:

• A. 1
• B. -2
• C. 2
• D. -1
• E. \( \sqrt{3} \)

Hint:

To find the slope of a line perpendicular to another line, take the negative reciprocal of the original slope.

Answer 1

The Correct Option is C

Step 1: The slope of line \( PQ \) is given by: \[ m_{PQ} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 4}{3 - (-3)} = \frac{-3}{6} = -\frac{1}{2} \] Step 2: The slope of the line perpendicular to \( PQ \) is the negative reciprocal of \( m_{PQ} \). 
Hence: \[ m_{{perpendicular}} = -\frac{1}{-\frac{1}{2}} = 2 \]