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Points A, B, C, and D are located on a line. A is at (-6,13), D is at (2,14), C is the midpoint of AD and B is the midpoint of AC. What is the sum of the coordinates of point B? Express the answer as a common fraction.

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sqdancefan

Answer:

  37/4

Step-by-step explanation:

The sum of the coordinates of point B is the weighted average of the sum of coordinates of points A and D. Those sums are A=-6+13 = 7; D=2+14=16.

Point B is 3/4 of the way from point D to point A, so the sum of its coordinates will be ...

  (3×7 +1×16)/4 = 37/4

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The coordinates of point B are (-4, 13.25), so their sum is 9.25 = 37/4.

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