Given:

The sides AB, BC and CA of a triangle ABC are as follows:

5x − 3y + 2 = 0 … (1)

x − 3y − 2 = 0 … (2)

x + y − 6 = 0 … (3)

To find:

The equation of the Altitude through the vertex A.

Concept Used:

Point of intersection of two lines.

Explanation:

Solving (1) and (3):

x = 2 , y = 4

Thus, AB and CA intersect at A (2, 4).

Let AD be the altitude.

AD⊥BC

∴ Slope of AD × Slope of BC = −1

Here, slope of BC = slope of the line (2) = 1/3

∴ Slope of AD×1/3 = - 1 ⇒ Slope of AD = - 3

Hence, the equation of the altitude AD passing through A (2, 4) and having slope −3 is y - 4 = - 3x - 2⇒ 3x + y = 10