I got the same answer, using A at (0,0), B at (1,0), so the midpoint at (.5,0). That gave me the new position of the midpoint at (0.705882352,0), which looks most like the third (correct) answer. But the coefficients given in the hint, 1/10 A, 8/10 B and 8/10 C don't add up to 1. I think the denominators should be 17, not 10. And 8/17 of the way between the initial position of the midpoint and B is (0.73529411,0), quite further to the right than the answer I got.
I got the same answer, using A at (0,0), B at (1,0), so the midpoint at (.5,0). That gave me the new position of the midpoint at (0.705882352,0), which looks most like the third (correct) answer. But the coefficients given in the hint, 1/10 A, 8/10 B and 8/10 C don't add up to 1. I think the denominators should be 17, not 10. And 8/17 of the way between the initial position of the midpoint and B is (0.73529411,0), quite further to the right than the answer I got.