Question

Find the angle between the lines x+2y+2 = 0 and 2x-y+1 = 0.

Answer 1

ax+by+c=0 => slope= (-a/b)x+2y+2=0  => slope= -1/2 ————> (m1)2x-y+1=0  => slope= 2/1 —————> (m2)tan(theta)= |m1 - m2| / 1+ (m1xm2)

           => | (-1/2) - 2| / 1+(-1/2)x2                      =>  5/2 / 0 (not defined)[tan(π/2) = not definedso, theta = π/2 therefore angle between them is 90°.              

Answer 2

slope of line x + 2y + 2 = 0 is m₁ = -1/2

slope of line 2x - y + 1 = 0 is m₂ = 2

\(\because\) m₁m₂ = -1/2 x 2 = -1

\(\therefore\) Both lines are perpendicular to each other.

\(\therefore\) Angle between both given lines is 90°.

Answer 3

Angle between two lines is |(m1 - m2)|/|(1+m1m2)| where | | belongs to modulus  

Slope of line 1:-  x+2y+2= 0

                               M1 = -1/2

Slope of line 2 :- 2x-y+1 =0

                               M2 = 2

Acc to formula tan theta = (-1/2 - 2)/(1+(-1/2)(2))

Tan theta = (-5/2)/0

Which is tan theta = undefined

So theta is equal to 90⁰

So both lines are perpendicular to each other