Question

Find the angle between the following lines: 3x-y+5= 0 and x - 2y-4=0​

Answer 1

Answer:

θ = 45°

Step-by-step explanation:

property used:

If θ is the angle between two intersecting lines defined by y₁= m₁x₁+c₁ and y₂= m₂x₂+c₂, then, the angle θ is given by

tanθ=±(m₂-m₁) / (1+m₁m₂)

line1 => 3x-y+5= 0  => y = 3x+5  

line2 => x - 2y-4=0​​ => 2y = x-4 => y = $\frac{x}{2}$- $\frac{4}{2}$=> y = $\frac{x}{2}$- 2

here,

m₁ = 3 , m₂ = $\frac{1}{2}$

=> tanθ = $\frac{| 3 - \frac{1}{2} |}{1+3*(\frac{1}{2} )}$

            =  $\frac{| \frac{6-1}{2} |}{\frac{2+3}{2} }$ = $\frac{| \frac{5}{2} |}{\frac{5}{2} }$

            = 1

here, tanθ = 1

but we know, tan 45° = 1

=> θ = 45°