Given:
Points (2, 0), (0, 3) and the line x + y = 1.
Let us assume A (2, 0), B (0, 3) be the given points.
Now, let us find the slopes
Slope of AB = m1
= [(3 - 0) / (0 - 2)]
= -3/2
Slope of the line x + y = 1 is -1
∴ m2 = -1
Let θ be the angle between the line joining the points (2, 0), (0, 3) and the line
x + y = tan θ = |[(m1 – m2) / (1 + m1m2)]|
= [(-3/2 + 1) / (1 + 3/2)]
= 1/5
θ = tan-1 (1/5)
∴ The acute angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1 is tan-1 (1/5).
