There are several ways you can get there. One is to find point D that bisects AB, then bisect DB to find point C.
... D = (A+B)/2 = (-10+6, -6+2)/2 = (-4, -4)/2 = (-2, -2)
... C = (D+B)/2 = (-2+6, -2+2)/2 = (4, 0)/2
... C = (2, 0)
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Another way is to find the weighted average of the given point values. The weights are the reverse of the relative segment lengths.
... C = (1/4)A + (3/4)B = (-10, -6)/4 +(3*6, 3*2)/4 = ((-10+18)/4, (-6+6)/4)
... C = (2, 0)
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You can find the vector AB and add 3/4 of that to A.
... AB = B - A = (6 -(-10), 2 -(-6)) = (16, 8)
... C = A + (3/4)AB = (-10, -6) + (3/4)(16, 8) = (-10 +12, -6 +6)
... C = (2, 0)
