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# Midpoint of a line segment

The point A lies on the line y=2X and the point B lies on the line y=x+3. The coordinates of the mid-point of AB are (2,6). What are the coordinates of A and of B ?

Ans: A(5 , 10) B(-1 , 2)

## 3 Answers By Expert Tutors

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Tutor
4.9 (365)

Experienced Calculus Instructor Vivian L.

Hi Joe;
This is an excellent answer.  However, there is one thing I do not understand.  If the points intersect at (3,6), how can the mid-point be at (2,6)?
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02/02/14 Joe P.

tutor
Vivian,
You are correct that the two graphs intersect at (3,6) but that doesn't prevent the possibility of a midpoint between to points on those lines being somewhere else.

For example, graph y = 0 and x = 0 our two axis lines.  They intersect at (0,0).  However, the point (1,1) could be a midpoint between the two lines, for points (2, 0) and (0, 2).  Point (2, 2) could also be a midpoint between (4, 0) and (0, 4).  There is actually an infinite number of possible midpoints for my example and the all lie on the y = x line.  Your problem also has an infinite number of midpoints between the two lines, (2, 6) is just one of them.
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02/03/14 Tutor
3 (1)

Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH Parviz F.

Hi Vivian : It is asking the midpoint of 2 points on each line, doesn't have to do anything with their intersecting point.
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02/03/14 Tutor
4.8 (4)

Mathematics professor at Community Colleges

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