The angle between the lines x – 2y = y and y – 2x = 5 is
Answers
EXPLANATION.
Angle between the lines,
⇒ x - 2y = 2.
⇒ y - 2x = 5.
As we know that,
Slope of the line : y = mx + c.
Equation : x - 2y = 2.
⇒ x = 2 + 2y.
⇒ x - 2 = 2y.
⇒ x/2 - 2/2 = y.
Slope = M₁ = 1/2.
Equation : y - 2x = 5.
⇒ y = 5 + 2x.
Slope = M₂ = 2.
As we know that,
Formula of angle between the lines,
⇒ tan∅ = | m₁ - m₂/1 + m₁m₂|
⇒ tan∅ = | 1/2 - 2/1 + (1/2)(2) |.
⇒ tan∅ = | 1 - 4/2/1 + 1 |.
⇒ tan∅ = | -3/2/2 |.
⇒ tan∅ = | -3/4 |.
⇒ tan∅ = 3/4.
⇒ ∅ = tan⁻¹(3/4).
MORE INFORMATION.
(1) = Distance between two parallel lines.
ax + by + c₁ = 0 & ax + by + c₂ = 0 then,
d = | c₁ - c₂/√a² + b² |.
(2) = Condition of concurrency.
Angle between the lines are :
- x - 2y = 2.
- y - 2x = 5.
We know :
• Slope of the line : y = mx + c
Equation : x - 2y = 2
⇒ x = 2 + 2y
⇒ x - 2 = 2y
⇒ x/2 - 2/2 = y
• Slope = M₁ = 1/2
Equation : y - 2x = 5
⇒ y = 5 + 2x
• Slope = M₂ = 2
We know that,
Formula of angle between the lines,
⇒ tan∅ = | m₁ - m₂/1 + m₁m₂|
⇒ tan∅ = | 1/2 - 2/1 + (1/2)(2) |
⇒ tan∅ = | 1 - 4/2/1 + 1 |
⇒ tan∅ = | -3/2/2 |
⇒ tan∅ = | -3/4 |
⇒ tan∅ = 3/4
⇒ ∅ = tan⁻¹(3/4)