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 is
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