# 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. $$\color{blue}{(– 2, – 3), (3, – 6)}$$

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. $$\color{blue}{(0.5, –4.5)}$$