Question
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Points , and are on a line such that is
between and , and is between and . The
distance from to is 6 units. The distance from
to is twice the distance from to , and the
distance from to is twice the distance from to
. What is the distance, in units, from the midpoint
of to the midpoint of ?

Ask by Clark Love. in the United States
Feb 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The distance from the midpoint of segment BC to the midpoint of segment CD is 18 units.

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Answered by UpStudy AI and reviewed by a Professional Tutor

Mind Expander

To solve the problem, we need to determine the positions of points , , , and on the line based on the given distances.
  1. The distance from to is given as 6 units:
    Thus, if we set at position 0, then is at position 6.
  2. The distance from to is twice the distance from to :
    Therefore, is at position:
  3. The distance from to is twice the distance from to :
    Thus, is at position:
Now, we find the midpoints of and .
  • The midpoint of :
  • The midpoint of :
Finally, we find the distance from the midpoint of to the midpoint of :
Thus, the distance from the midpoint of to the midpoint of is units.

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