Question

The figure alongside (not drawn to scale) represents the lines y = x + 1 and y = `sqrt(3)x - 1`.

(i) Find the angle which the line y = x + 1 makes with X-axis.

(ii) Find the angle which the line y = `sqrt(3)x - 1` makes with X-axis.
(iii) Determine angle θ.
(iv) Find the point where the line y = x + 1 meets X-axis.
(v) Find the point where the line y = `sqrt(3) x - 1` meets Y-axis.

Answer 1

(i) y = x + 1
⇒ m₁ = tan θ₁ = 1 = tan 45°
⇒ θ₁ = 45°.
(ii) y = `sqrt(3) x - 1`
⇒ m₂ = tan θ₂ = `sqrt(3)` = tan 60°
⇒ θ₂ = 60°
(iii) ∴ θ = θ₂ - θ₁.
(∵ Exterior ∠ = Sum of interior opposite ∠s)
= 60° - 45° = 15°.
(iv) Put y = 0 in y = x + 1, we get
0 = x + 1
⇒ x = -1
∴ The required points is (-1, -0).
(v) Put x = 0 in y = `sqrt(3)x - 1`, we get y = -1
∴ The required point is (0, -1).