Question 1146038
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The statement of the problem is incomplete.  The solution will be different, depending on the order of the four points.<br>
To solve the problem, we have to assume a particular order of the four points.  It is probable that the points A, B, C, and D are in that order; but the statement of the problem should specify that.<br>
Assuming the order A-B-C-D, we can then find a solution as follows.<br>
AB:AC = 7:10, so let AB = 7x and AC = 10x; that makes BC = 3x<br>
BD:CD = 9:2, so let BD = 9y and CD = 2y; that makes BC = 7y<br>
Then, CD = 9 and BC:CD = 7y:2y = 7:2 makes BC equal to (7/2)*9 = 31.5<br>
And then BC = 31.5 and AB:BC = 7x:3x = 7:3 makes AB equal to (7/3)*31.5 = 73.5<br>
ANSWER: AB = 73.5