find the angle between the lines 3x +y-7=0 and x+2y+9=0 - Maths - Straight Lines

Question

find the angle between the lines 3x +y-7=0 and x+2y+9=0

Ankush Jain · Accepted Answer

The equations of two straight lines are:

3x + y -7 = 0 and x + 2y + 9 = 0

Let m₁ and m₂ be the slope of these two lines. Then,

m₁ = $- \frac{c o e f f . o f x}{c o e f f . o f y} = \frac{- 3}{1}$ and m₂ = $- \frac{c o e f f . o f x}{c o e f f . o f y} = \frac{- 1}{2}$

Let θ be the angle between two lines. Then,

tan θ = $| \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} | = | \frac{- 3 + \frac{1}{2}}{1 + (- 3) (\frac{- 1}{2})} |$

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

⇒ tan θ = 1

⇒ θ = tan^-11 = $\frac{π}{4}$