anonymous
  • anonymous
If M (6,8) is the midpoint of line segment AB, and if A has coordinates (2,3) , find the coordinates of B.
Mathematics
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SOLVED
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chestercat
  • chestercat
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sasogeek
  • sasogeek
i did a similar work today in class... lemme see if i can solve it
mathteacher1729
  • mathteacher1729
Have you tried sketching this out on a piece of graph paper? That is probably the easiest way to solve it. If you know (6,8) is the midpoint, and (2,3) is one of the endpoints, then it should be a matter of just plotting those two, and finding the other endpoint. :)
sasogeek
  • sasogeek
I believe its related to vectors...

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anonymous
  • anonymous
thanks! and i have never heard of a vector, but thanks anyway
sasogeek
  • sasogeek
cordinates of B(x,y)=(10,13)
anonymous
  • anonymous
Graphing is one way to do the problem. But sometimes, graphing it is hard to do. So here’s an algebraic method. If M(m1, m2) is the midpoint of two points A(x1, y1) and B(x2, y2), then m1 = (x1 + x2)/2 and m2 = (y1 + y2)/2. In other words, the x-coordinate of the midpoint is the average of the x-coordinates of the two points, and the y-coordinate of the midpoint is the average of the y-coordinates of the two points. Let B have coordinates (x2, y2) in our problem. Then we have that 6 = (2 + x2)/2 and 8 = (3 + y2)/2. Solving for the coordinates gives x2 = 10, y2 = 13.
mathteacher1729
  • mathteacher1729
Excellent answer, Verify. This method works for all points, even very large ones which may be difficult or impossible to graph on a piece of paper. Example: find endpoint A if midpoint M(-232, 42) and point B(100,-34). I recommend trying BOTH methods for the original problem given by Loverslane -- graph it, and then verify your graph with the formula. Now try solving the problem I gave in the example. Graphing will not work, but the formula will! :)
sasogeek
  • sasogeek
I answered that using the vector method but yh, that's other way to solve it though :) i guess it run down to the same answer. I wouldn't bother to explain the vector method since you're not familiar with vectors

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