The angle the line joining the given points make with the positive direction of the x-axis is 341.56°
The angle Ф between two points (x₁,y₁) and (x₂,y₂) is gotten from tanФ = (y₂ - y₁)/(x₂ - x₁).
Since (x₁, y₁) = (3b, a) and (x₂, y₂) = (3a, b)
Substituting the values of the variables into the equation, we have
tanФ = (y₂ - y₁)/(x₂ - x₁)
tanФ = (b - a)/(3a - 3b)
tanФ = -(a - b)/3(a - b)
tanФ = -1/3
taking inverse tan of both sides, we have
Φ = tan⁻¹(-1/3)
Φ = -tan⁻¹(1/3)
Φ = -18.43°
Converting to a positive angle, we have
Φ = -18.43° + 360°
Φ = 341.56°
So, the angle the line joining the given points make with the positive direction of the x-axis is 341.56°
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