Question

The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is
(a) π/4
(b) π/6
(c) π/3
(d) 3 π/4
(e) 5 π/6

Answer 1

(d) $\raisebox{1ex}{$3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

The midpoint of the line joining the points (4, −5) and (−2, 9) is (1, 2).

Let $\theta$ be the inclination of the straight line passing through the points (−3, 6) and (1, 2).

$$\begin{gathered} \mathrm{Then,}\tan \theta =\frac{2-6}{1+3}=-1 \\ \Rightarrow \theta =\frac{3\mathrm{\pi }}{4} \end{gathered}$$