Finding Midpoint

Finding Midpoint

Learn how to find the midpoint of a line segment when you are given two endpoints.

  • The middle of a line segment is its midpoint.
  • The Midpoint of two endpoints A \((x_{1},y_{1})\) and B \((x_{2},y_{2})\) can be found using this formula: M \(\color{blue}{(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})}\)

Example 1:

Find the midpoint of the line segment with the given endpoints. \((1, -2), (3, 6)\)

Solution:

Midpoint \(= (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) → (x_{1},y_{1} )(1,-2)\) and \((x_{2},y_{2} )=(3,6)\)
Midpoint \(=(\frac{1 + 3}{2},\frac{-2+6}{2}) → (\frac{4}{2},\frac{4}{2}) → M(2,2) \)

Example 2:

Find the midpoint of the line segment with the given endpoints. \((-2, 5) , (8, -3)\)

Solution:

Midpoint \(=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) → (x_{1},y_{1 })=(-2,5) and (x_{2},y_{2} )=(8,-3)\)
Midpoint \(=(\frac{-2 + 8}{2},\frac{5-3}{2}) → (\frac{6}{2},\frac{2}{2}) → M(3,1)\)

Example 3:

Find the midpoint of the line segment with the given endpoints. \((4,-5),(0,9)\)

Solution:

Midpoint \(=( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) → (x_{1},y_{1} )=(4,-5) and (x_{2},y_{2} )=(0,9)\)
Midpoint \(=(\frac{4 + 0}{2},\frac{-5+9}{2}) → (\frac{4}{2},\frac{4}{2}) → M(2,2) \)

Example 4:

Find the midpoint of the line segment with the given endpoints. \((6,7),(4,-5)\)

Solution:

Midpoint \(=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) → (x_{1},y_{1} )=(6,7)\) and \((x_{2},y_{2} )=(4,-5)\)
Midpoint \(=(\frac{6 + 4}{2},\frac{7-5}{2}) → (\frac{10}{2},\frac{2}{2}) → (5,1)\)

Exercises

Find the midpoint of the line segment with the given endpoints.

  1. \(\color{blue}{(2, – 2), (3, – 5)}\)
  2. \(\color{blue}{ (0, 2), (– 2, – 6) }\)
  3. \(\color{blue}{ (7, 4), (9, – 1)}\)
  4. \(\color{blue}{ (4, – 5), (0, 8)}\)
  5. \(\color{blue}{(1, – 2), (1, – 6)}\)
  6. \(\color{blue}{(– 2, – 3), (3, – 6)}\)

Download Finding Midpoint Worksheet

  1. \(\color{blue}{(2.5, –3.5)}\)
  2. \(\color{blue}{(–1, –2)}\)
  3. \(\color{blue}{(8, 1.5)}\)
  4. \(\color{blue}{(2, 1.5)}\)
  5. \(\color{blue}{(1, –4)}\)
  6. \(\color{blue}{(0.5, –4.5)}\)

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