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The vertices of a triangle are A(13,13), B(9,3), and C(-1,1).

Determine the equation of the median AM, where M is the midpoint of BC.

Midpoint M of BC = ((9-1)/2,(3+1)/2)
=(4,2)
slope AM = (13-2)/(13-4) = 11/9

So the equation of the median is
11x - 9y + c = 0, (knowing that the slope of Ax + By + C = 0 is -A/B)

substitute one of the points, say (4,2)
11(4) - 9(2) + C = 0
C=-26

the equation of the median is 11x - 9y - 26 = 0


I use this method of finding the equation of a straight line if the slope is a fraction.
It gives the equation very quickly in the general form without any fractions.

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