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A (2, – 4), B (3, 3) and C (– 1, 5) are the vertices of triangle ABC.

Find the equation of: the altitude of the triangle through B.

Answer:

**Solution:**

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.

Given, A (2, – 4), B (3, 3) and C (– 1, 5) are the vertices of triangle ABC

D is the mid-point of BC

So, the co-ordinates of D will be

((3 – 1)/2, (3 + 5)/2) = (2/2, 8/2) = (1, 4)

Now,

The slope of AC (m_{1}) = (5 + 4)/ (-1 – 2) = 9/-3 = -3

Let the slope of BE be m_{2}

Then, m_{1} x m_{2} = -1

-3 x m_{2} = -1

m_{2} = 1/3

so, the equation of BE will be

y – 3 = 1/3 (x – 3)

3y – 9 = x – 3

x – 3y + 6 = 0

**Thus, the required line equation is x – 3y + 6 = 0.**

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