First slide

Equation of line in Straight lines

Question

The inclination of the straight line passing through the point $A (- 3, 6)$ and the mid-point of the line joining the $B (4, - 5)$ and $C (- 2, 9)$ , with $x -$ axis is

Easy

A

$\frac{π}{4}$
B

$\frac{π}{6}$
C

$\frac{π}{3}$
D

$\frac{3 π}{4}$

Solution

The coordinates of the mid-point $D$ of line segment $B C$ are $(1, 2) .$
$∴$ Slope of $A D = \frac{6 - 2}{- 3 - 1} = - 1$
$\Rightarrow \tan θ = - 1$ , where $θ$ is the angle made by $A D$ with $x -$ axis
$\Rightarrow θ = \frac{3 π}{4}$
So, $A D$ makes angle $\frac{3 π}{4}$ with $x -$ axis.

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