Find the angle of inclination of the line passing through the points

(i) (1, 2) and (2, 3) (ii) and (0, 0)

(iii) (a, b) and (–a, –b)

Slope of straight line passing through the points (x₁, y₁) and (x₂, y₂) is given by

i) Slope of straight line passing through the points (1, 2) and (2, 3) is

m = 1

If θ is the angle of inclination of the line, then the slope of the line is

m = tan θ where 0° ≤ θ ≤ 180°, θ ≠ 90°

∴ tan θ = 1 ⇒ θ = 45°

ii) Slope of straight line passing through the points (3, √3) and (0, 0) is

m = √3

If θ is the angle of inclination of the line, then the slope of the line is

m = tan θ where 0° ≤ θ ≤ 180°, θ ≠ 90°

∴ tan θ = √3 ⇒ θ = 30°

iii) Slope of straight line passing through the points (a, b) and (–a, –b) is

If θ is the angle of inclination of the line, then the slope of the line is

m = tan θ where 0° ≤ θ ≤ 180°, θ ≠ 90°

∴