The equations of the sides `A B ,\ B C\ a n d\ C A\ of\ `triangleA B C`\ a r e\ y-x=2,\ x+2y=1\ a n d\ 3x+y+5=0` respectively. The equation of the altitude through B is `x-3y+1=0` b. `x-3y+4=0` c. `3x-y+2=0` d. none of these

Explanation

To find the equation of the altitude through point B of triangle ABC, we will follow these steps:

### Step 1: Identify the equations of the sides of the triangle
The equations of the sides of triangle ABC are given as:
1. \( AB: y - x = 2 \) (or \( y = x + 2 \))
2. \( BC: x + 2y = 1 \) (or \( 2y = 1 - x \) or \( y = \frac{1 - x}{2} \))
3. \( CA: 3x + y + 5 = 0 \) (or \( y = -3x - 5 \))

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