The given figure represents the lines y = x + 1 and y = Write down the angles which the lines make with the positive direction of the x-axis. Hence, determine θ.

Question

KnowledgeBoat · Accepted Answer

Given, y = x + 1 and y = . Comparing equations with y = mx + c we get, m₁ = 1 and m₂ = . Let the first line make angle θ₁ and second make θ₂ with positive direction of x-axis. The inclination that y = x + 1 makes is, ⇒ m₁ = tan θ₁ = 1 ⇒ tan θ₁ = 1 = tan 45° ⇒ tan θ₁ = tan 45° ⇒ θ₁ = 45°. The inclination that y = - 1 makes is, ⇒ m₂ = tan θ₂ = ⇒ tan θ₂ = = tan 60° ⇒ tan θ₂ = tan 60° ⇒ θ₂ = 60°. From graph we get, 60° is the exterior angle. We know that, Exterior angle = Sum of two opposite interior angles. ∴ 60° = θ + 45° ⇒ θ = 60° - 45° ⇒ θ = 15° Hence, y = x + 1 makes 45° and y = makes 60° with the x-axis. The value of θ = 15°.

Mathematics

The given figure represents the lines y = x + 1 and y = Write down the angles which the lines make with the positive direction of the x-axis. Hence, determine θ.

Straight Line Eq

Related Questions

The equation of the line PQ is 3y - 3x + 7 = 0.
(i) Write down the slope of the line PQ.
(ii) Calculate the angle that the line PQ makes with the positive direction of x-axis.

Mathematics

The given figure represents the lines y = x + 1 and y = Write down the angles which the lines make with the positive direction of the x-axis. Hence, determine θ.

Straight Line Eq

Related Questions

The equation of the line PQ is 3y - 3x + 7 = 0.(i) Write down the slope of the line PQ.(ii) Calculate the angle that the line PQ makes with the positive direction of x-axis.

The equation of the line PQ is 3y - 3x + 7 = 0.
(i) Write down the slope of the line PQ.
(ii) Calculate the angle that the line PQ makes with the positive direction of x-axis.