what will happen to the slope angle if coordinate points changes?

Question

Here is the figure:

Now the slope angle is calculated as:
slope angle \begin{align} \theta = \tan^{-1}(\frac{Y2 - Y1}{X2 - X1}) \end{align}

Now if I change the notations of point A and B as:

then which angle will the $\theta$? Will it be same or 180 minus the previous $\theta$?

Please let me know what angle will I get as per second figure.

Answer 1

There are two bits of fundamentals that may be causing you some confusion.

One, the angle of inclination is the angle measured by rotating counter-clockwise from the horizontal. Suppose you have a horizontal line $\ell$. The angle that you must rotate counter-clockwise to make $\ell$ parallel to your given line is the angle of inclination.

Two, a little bit of work dealing with algebra: $$\frac{a-b}{c-d}=\frac{-(b-a)}{-(d-c)}=\frac{b-a}{d-c}.$$ As it appears, it does not matter which set of coordinates you denote as $A$ or $(x_1,y_1)$ or what have you.