# The equations of the sides AB, BC and CA of ΔABC are y – x = 2, x + 2y = 1 and 3x + y + 5 = 0 respectively. The equation of the altitude through B isA. x – 3y + 1 0B. x – 3y + 4 = 0C. 3x – y + 2 = 0D. none of these

The equation of the sides AB, BC and CA of ABC are y x = 2, x + 2y = 1 and 3x + y + 5 = 0, respectively.

Solving the equations of AB and BC, i.e. y x = 2 and x + 2y = 1, we get:

x = 1, y = 1

So, the coordinates of B are ( 1, 1).

The altitude through B is perpendicular to AC.

Slope of AC = -3

Thus, slope of the altitude through B is 13.

Equation of the required altitude is given below:

y – 1 = 13x + 1

x – 3y + 4 = 0

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