Altitude: A line drawn from the vertex that meets the opposite side at right angles. It determines the height of the triangle.

In triangle ABC, let the altitudes from vertices A, B and C are AL, BM and CN on sides BC,AC and AB respectively.

Now we will find slope of sides and using the relation between the slopes of perpendicular lines i.e. m1.m2 = - 1 we will find the slopes of altitudes.

Now equation of altitudes using two point form

For altitude AL,

y - ( - 2) = - 2(x - 2)

y + 2 + 2x - 4 = 0

2x + y - 2 = 0

For altitude BM,

y - 1 = - 1(x - 1)

y - 1 + x - 1 = 0

x + y - 2 = 0

For altitude CN,

3y = x + 1

x - 3y + 1 = 0

So, the required equations of altitudes are for AL: 2x + y - 2 = 0

For BM: x + y - 2 = 0

For CN: x - 3y + 1 = 0