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Question 336735: Points X and Y are the endpoints of a line segment, and the length of the segment is less than 25. There are five other points on the line segment, R, S, T, U, and V, which are located at distances of 1, 3, 6, 10, and 13, respectively, from point X. Which of the points could be the midpoint of XY ?
(A)R (B) S (C) T (D) U (E) V
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
Here is a line which is 25 units long, with all the points except Y
marked. The point Y is somewhere beyond V but not all the way to the
right end, since XY is less than 25 units and the line drawn is 25 units.
I'll mark two more points on the line, A and B. I'll put A
2 units from X and B 12 units from X
The correct answer is not R because XR is 1 and XA is 2, so
R is the midpoint of XA, not XY, for Y must be beyond V.
The correct answer is not S because XS is 3 and XT is 6, so
S is the midpoint of XT, not XY, for Y must be beyond V.
The correct answer is not T because XT is 6 and XB is 12, so
T is the midpoint of XB, not XY, for Y must be beyond V.
The correct answer is not V because XV is 13 and since 2x13 = 26
V would have to be the midpoint of a line 26 units long and the
line drawn is only 25 units long.
So that only leaves point U, and it will be the midpoint of XY
if Y is 20 units from X, so now we know where Y is located, and
we can shorten the line:
The answer is V
Edwin
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