Q. 51

# In a triangle ABC with vertices A(2,3) B(4,-1) and C(-1,2), find the equation and length of the altitude from the vertex A.

Equation of the line joining the points B(4,-1) and C(-1,2)

5(y+1) = -3(x-4)

5y+5 = -3x+12

5y+3x=7

Equation of the altitude from A would be of the form

3x-5y+k = 0

Since point A(2,3) passes through this equation

3(2)-5(3) +k = 0

k = 9

Therefore the equation of the altitude is = 3x-5y+9 = 0

Length of the altitude =

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