Question

Find the angle that the line through the given pair of points makes with the positive direction of the x-axis

(1,4) and (-1,2)

Answer 1

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

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

`Slope(AB)=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

Substituting the values we get

`Slope(AB)=(2-4)/(-1-1)=(-2)/(-2)=1\\\\Slope=1`

Also Slope of line when angle ' θ ' is given as

`Slope=\tan \theta`

Substituting Slope = 1 we get

`1=\tan \theta`

`\tan \theta=1\\\theta=\tan^(-1)(1)`

We Know That for angle 45°,

tan 45 = 1

Therefore

`\theta=45\°`

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.