Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).

Given points are A(5, 2), B(2,3) and C(3, -1)

Firstly, we find the slope of the line joining the points (2,3) and (3, -1)

It is given that line passing through the point (5,2) is perpendicular

to BC

∵ m₁m₂ = -1

⇒ -4 × m₂ = -1

Now, we have to find the equation of line passing through point (5,2)

Equation of line: y – y₁ = m(x – x₁)

⇒ 4y – 8 = x – 5

⇒ x – 5 – 4y + 8 = 0

⇒ x – 4y + 3 = 0

Hence, the equation of line passing through the point (5,2) is x – 4y + 3 = 0