Question

find the angle between the x-axis and the line joining the points (3,-1)and (4,-2)​

Answer 1

Let A(3,-1) and B(4,-2) be the given points  

and we will consider m be the slope of the line AB.

m = -2-(-1)/4-3

= -2 + 1/1

= -1

[∴ m = (y₂ - y₁) / (x₂ - x₁)]

Now we will consider θ = m = -1

= - tan 45°

= tan (180° - 45°)

= tan 135°

θ = 135°

So the required angle is 135°

Answer 2

SOLUTION

Slope of x-axis = 0

m1= 0

slope of line joining the points(3,-1) &

(4,-2)

$= > \frac{ - 2 - ( - 1)}{4 - 3}$

m2= -2+1/4-3

=) m2= -1

Angle between these two lines is given by,

$tan \theta = \frac{m2 - m1}{1 + m1m2} \\ \\ = > tan \theta = \frac{ - 1 - 0}{1 + ( - 1) \times 0} \\ \\ = > tan \theta = - 1 \\ \\ = > tan \theta = - tan \frac{\pi}{4} \\ \\ = > tan \theta = tan(\pi - \frac{\pi}{4} ) \\ \\ = > \theta = \frac{3\pi}{4}$

theta= 3× 180°/4

=) theta= 3× 45°

=) theta= 135°

Thus, angle between x - axis and the line is 135°.

hope it helps ☺️⬆️