# Find the equation

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

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