Question

find the angle made by the line joining (5,3) and (-1,-3) with the positive direction of X axis.

Answer 1

Slope=(y2-y1) /(x2-x1)
m=(-3-3)/(-1-5)
m=-6/-6
m=1
Tan theta=m
Tan theta=1=45°
theta=45°

Answer 2

The angle made by the line joining (5,3) and (-1,-3) with the positive direction of X axis is 45°

Given :

The points (5,3) and (-1,-3)

To find :

The angle made by the line joining (5,3) and (-1,-3) with the positive direction of X axis

Solution :

Solution :Step 1 of 3 :

Find slope of the line

Here the given points are (5,3) and (-1,-3)

The slope of the line joining (5,3) and (-1,-3)

$\displaystyle \sf{ = \frac{3 - ( - 3)}{5 - ( - 1)} }$

$\displaystyle \sf{ = \frac{3 + 3}{5 + 1} }$

$\displaystyle \sf{ = \frac{6}{6} }$

$\displaystyle \sf{ =1}$

Step 2 of 3 :

Form the equation

Let θ be the angle made by the line with the positive direction of X axis

By the given condition

tan θ = 1

Step 3 of 3 :

Find the angle

tan θ = 1

⇒ tan θ = tan 45°

⇒ θ = 45°

Hence the angle made by the line joining (5,3) and (-1,-3) with the positive direction of X axis is 45°