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Midpoint formula review

Review the midpoint formula and how to apply it to solve problems.

What is the midpoint formula?

The formula gives the midpoint of the points (x1,y1) and (x2,y2) in the coordinate plane:
(x1+x22,y1+y22)
Want to learn more about the midpoint formula? Check out this video.

What problems can I solve with the midpoint formula?

Given two points on the plane, you can find their midpoint. For example, let's find the midpoint of (5,3) and (1,7):
=(x1+x22,y1+y22)=(5+12,3+72)Plug in coordinates=(3,5)
Notice: we were careful to put the x-coordinates together and the y-coordinates together and not mix them up.

Check your understanding

Problem 1
What is the midpoint of (6,2) and (10,0)?
Choose 1 answer:

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

  • blobby green style avatar for user mohnzy02
    How do you find the endpoint of a line when you are given the other endpoint and the midpoint?
    (15 votes)
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    • hopper cool style avatar for user Seed Something
      Great question, and it's definitely a situation we need to be able to solve.

      When we are given the Midpoint and an Endpoint, and asked to find the Other Endpoint.

      We can still use the concepts from the Midpoint Formula by plugging in the information we do have, because…

      we normally find the Midpoint by adding the corresponding coordinates, then dividing by two…

      (first endpoint + second endpoint) divided by two = Midpoint

      So, we know that…
      (x1 + x2)/2 = Midpoint x
      and that…
      (y1 + y2)/2 = Midpoint y

      the given Endpoint (x, y) can be plugged into either the first or second x and y locations because addition is Commutative, (it's rearrangeable), so it doesn't matter which end values are first or second,

      and the given Midpoint, (x or y), is placed as equal to the Endpoint addition then division.

      Given:
      Endpoint (3, 5)
      Midpoint (7, 10
      )

      •Find Other Endpoint
      =
      (x1 + x2)/2 = Midpoint x
      and
      (y1 + y2)/2 = Midpoint y
      =
      (x + 3)/2 = 7
      and
      (y + 5)/2 = 10

      •Let's solve for x first:
      (x + 3)/2 = 7
      Multiply both sides by 2,
      to cancel the division on the left.
      =
      2((x + 3)/2) = 7 • 2
      =
      x + 3 = 14
      Subtract 3 from both sides,
      to isolate x on the left.
      =
      x + 3 -3 = 14 -3
      =
      x = 11 ←🥳

      •Solve for y the same way…
      (y + 5)/2 = 10
      =
      2((y + 5)/2) = 10(2)
      =
      y + 5 = 20
      =
      y = 20 -5
      =
      y = 15 ←🥳

      • Other Endpoint is at:
      (11, 15) ←🥳🥳

      •Each time the pattern of operations will be the same:
      Multiply the Midpoint coordinate by 2, then add or subtract the given Endpoint to isolate variable.

      2 • (Midpoint x or y) +/- (endpoint)
      =
      other endpoint


      •Be aware if a given Endpoint coordinate is negative, it will be added rather than subtracted to isolate the variable.

      (Example in Comments)

      (ㆁωㆁ)I hope this helps someone!
      (31 votes)
  • duskpin seed style avatar for user windham.brenaisha
    don't u divied when u do the midpoint
    (5 votes)
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  • aqualine ultimate style avatar for user khalikcarthon
    I think I might have lost a few braincells in the process
    ... :[
    (9 votes)
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  • blobby green style avatar for user Justice Clark
    how do i find coordinators if im looking for the endpoint
    (3 votes)
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    • mr pink green style avatar for user David Severin
      Are you saying you know one endpoint and the midpoint? If this is what you are asking, find the vector from the endpoint to the midpoint, the starting at midpoint, go along an equivalent vector. For example, endpoint is at (5,6) and midpoint is at (3,8) so the vector is <3-5, 8-6> or <-2,2>. SO starting at (3,8) along vector <-2,2), you end at (1,10).
      (10 votes)
  • blobby green style avatar for user Ella Mae Latinah Alvior
    formula for the length of scalene triangle
    (1 vote)
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  • blobby green style avatar for user ni064941
    what is length triangle mean?
    (2 votes)
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  • blobby green style avatar for user miquitaia
    How do you find the values of a and b when given the endpoints (1,a) and (b,-4) and the midpoint (4,-6)?
    (3 votes)
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  • duskpin seed style avatar for user K.B
    lowkey brain screaming - im still somewhat confused
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      The midpoint formula is just an average.
      Add the 2 X-values, then divide by 2.
      Add the 2 Y-values, then divide by 2.
      You have then found the average for the X and Y values which gives you the point half way between the original 2 points.
      (5 votes)
  • blobby green style avatar for user Jason Duran
    Plot two points to find me square in the above graph. Label the points R and S. A square is a quadrilateral with all for size of the same length. After planting the points trace to square by connecting the points
    (2 votes)
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  • duskpin seed style avatar for user Tenzin
    how do you find the midpoint of 3 coordinates
    (2 votes)
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