The slope of a line perpendicular to the line passing through the points P(3, –4) and Q(1, –8) is:

1. $\dfrac{-1}{2}$

2. 2

3. $\dfrac{1}{2}$

4. –2

Slope of the line passing through P(3, –4) and Q(1, –8).

$m${PQ} = \dfrac{y2 - y1}{x2 - x_1} \\[1em] = \dfrac{-8 - (-4)}{1 - 3} \\[1em] = \dfrac{-8 + 4}{-2} \\[1em] = \dfrac{-4}{-2} = 2.

Since the required line is perpendicular to line PQ, the product of their slopes must be -1.

Let slope of required line be m.

⇒ m_PQ × m = -1

⇒ 2 × m = -1

⇒ m = $\dfrac{-1}{2}$

Hence, option 1 is the correct option.