Question

Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1

Answer 1

Given: 

Points (2, 0), (0, 3) and the line x + y = 1. 

Assuming: 

Let A (2, 0), B (0, 3) be the given points. 

To find: 

Angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1. 

Explanation:

Slope of AB = m₁ = \(\frac{3-0}{0-2}-=\frac{3}{2}\) 

Slope of the line x + y = 1 is -1 

∴ m₂ = -1 

Let θ be the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1

Hence, the acute angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1 is tan^-1\(\Big(\frac{1}{5}\Big)\)