Find the angle between the X-axis and the line joining the points… - Vidyadip

Question

Find the angle between the X-axis and the line joining the points (3, -1) and (4, -2).

✓

Answer

Slope of the line segment joining the points (3, -1) and (4, -2) is
$\text{m}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}=\frac{-2-(-1)}{4-3}=\frac{-2+1}{4-3}=\frac{-1}{1}=-1$
Slope of x axis is 0
$\Rightarrow\text{m}_2=0$
If $\theta$ is the angle between x axis and the line segment then
$\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$=\Big|\frac{-1-0}{1+(-1)(0)}\Big|$
$=\frac{-1}{1}=-1$
$\therefore\theta=135^\circ$

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