Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt
[tex]Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the values we get
[tex]Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1[/tex]
Also Slope of line when angle ' θ ' is given as
[tex]Slope=\tan \theta[/tex]
Substituting Slope = 1 we get
[tex]1=\tan \theta[/tex]
[tex]\tan \theta=1\\\theta=\tan^{-1}(1)[/tex]
We Know That for angle 45°,
tan 45 = 1
Therefore
[tex]\theta=45\°[/tex]
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
