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# Find the equation of the median of a triangle whose sides are given by the equations 3x+2y+6=0,2x-5y+4=0,x-3y-6=0

Arun
25763 Points
3 years ago
olving the equations 3x + 2y + 6 = 0 and 2x – 5y + 4 = 0 we get x = –2 and y = 0.
Solving the equations x – 3y – 6 = 0 and 2x – 5y + 4 = 0 we get x = –42 and y = –16.
Solving the equations 3x + 2y + 6 = 0 and x – 3y – 6 = 0 we get x = –6/11 and y = –24/11.
So let the intersection points be A, B and C i.e. the triangle be ABC.
Coordinates of A, B and C will be A(-2, 0); B(-42, -16) and C(-6/11, -24/11).
By mid-point formula the mid-point of AB will be (-22, -8)
Equation of line passing through this mid-point and the opposite vertex C(-6/11, -24/11) will be the equation of the median from C. The equation will be

16x - 59y -120 = 0.        (From two point form)

Similarily find the equations of median through A & B