## How to Find the Midpoint of a Line?

Midpoint is a point positioned in between $$2$$ points and it is in the middle of the line that joins these $$2$$ points. If the line is drawn to join these $$2 points, the midpoint is a point in the middle of the line and is equal distant from the \(2$$ points. Presented any $$2$$ points, say $$A$$ and $$B$$, the midpoint will be a point $$M$$ which is found halfway in between points $$A$$ and $$B$$. So, to determine the midpoint, you merely measure the length of the line segment and divide it by $$2$$.

### Midpoint Formula used in Math

Presented with $$2$$ points $$A(x_{1},y_{1})$$ and $$B(x_{2},y_{2})$$, the midpoint in between $$A$$ and $$B$$ is given by:

$$M(x_{3} \ , \ y_{3}) \ = \ (\frac{x_{1} \ + \ x_{2}}{2} \ , \ \frac{y_{1} \ + \ y_{2}}{2})$$

where, $$M$$ is the midpoint in between $$A$$ and $$B$$, and $$(x_{3} \ , \ y_{3})$$ are the coordinates.

### Exercises for Finding Midpoint

1) Find the midpoint of the line passing through $$(3,-3), (3,7)$$$$\ \Rightarrow \$$

2) Find the midpoint of the line passing through $$(-1,9), (5,-5)$$$$\ \Rightarrow \$$

3) Find the midpoint of the line passing through $$(-4,0), (4,2)$$$$\ \Rightarrow \$$

4) Find the midpoint of the line passing through $$(-4,-5), (-2,5)$$$$\ \Rightarrow \$$

5) Find the midpoint of the line passing through $$(-6,10), (4,-8)$$$$\ \Rightarrow \$$

6) Find the midpoint of the line passing through $$(-6,-4), (2,6)$$$$\ \Rightarrow \$$

7) Find the midpoint of the line passing through $$(-13,7), (7,-5)$$$$\ \Rightarrow \$$

8) Find the midpoint of the line passing through $$(-4,-3), (6,7)$$$$\ \Rightarrow \$$

9) Find the midpoint of the line passing through $$(-5,0), (5,4)$$$$\ \Rightarrow \$$

10) Find the midpoint of the line passing through $$(2,3), (-4,1)$$$$\ \Rightarrow \$$

1) Find the midpoint of the line passing through $$(3,-3), (3,7)$$$$\ \Rightarrow \ \color{red}{M = (\frac{3 \ + \ 3}{2}, \frac{2 \ + \ 7}{2})}$$$$\ \Rightarrow \ \color{red}{M = (3, 2)}$$
2) Find the midpoint of the line passing through $$(-1,9), (5,-5)$$$$\ \Rightarrow \ \color{red}{M = (\frac{2 \ + \ 5}{2}, \frac{2 \ + \ (-5)}{2})}$$$$\ \Rightarrow \ \color{red}{M = (2, 2)}$$
3) Find the midpoint of the line passing through $$(-4,0), (4,2)$$$$\ \Rightarrow \ \color{red}{M = (\frac{0 \ + \ 4}{2}, \frac{1 \ + \ 2}{2})}$$$$\ \Rightarrow \ \color{red}{M = (0, 1)}$$
4) Find the midpoint of the line passing through $$(-4,-5), (-2,5)$$$$\ \Rightarrow \ \color{red}{M = (\frac{-3 \ + \ (-2)}{2}, \frac{0 \ + \ 5}{2})}$$$$\ \Rightarrow \ \color{red}{M = (-3, 0)}$$
5) Find the midpoint of the line passing through $$(-6,10), (4,-8)$$$$\ \Rightarrow \ \color{red}{M = (\frac{-1 \ + \ 4}{2}, \frac{1 \ + \ (-8)}{2})}$$$$\ \Rightarrow \ \color{red}{M = (-1, 1)}$$
6) Find the midpoint of the line passing through $$(-6,-4), (2,6)$$$$\ \Rightarrow \ \color{red}{M = (\frac{-2 \ + \ 2}{2}, \frac{1 \ + \ 6}{2})}$$$$\ \Rightarrow \ \color{red}{M = (-2, 1)}$$
7) Find the midpoint of the line passing through $$(-13,7), (7,-5)$$$$\ \Rightarrow \ \color{red}{M = (\frac{-3 \ + \ 7}{2}, \frac{1 \ + \ (-5)}{2})}$$$$\ \Rightarrow \ \color{red}{M = (-3, 1)}$$
8) Find the midpoint of the line passing through $$(-4,-3), (6,7)$$$$\ \Rightarrow \ \color{red}{M = (\frac{1 \ + \ 6}{2}, \frac{2 \ + \ 7}{2})}$$$$\ \Rightarrow \ \color{red}{M = (1, 2)}$$
9) Find the midpoint of the line passing through $$(-5,0), (5,4)$$$$\ \Rightarrow \ \color{red}{M = (\frac{0 \ + \ 5}{2}, \frac{2 \ + \ 4}{2})}$$$$\ \Rightarrow \ \color{red}{M = (0, 2)}$$
10) Find the midpoint of the line passing through $$(2,3), (-4,1)$$$$\ \Rightarrow \ \color{red}{M = (\frac{-1 \ + \ (-4)}{2}, \frac{2 \ + \ 1}{2})}$$$$\ \Rightarrow \ \color{red}{M = (-1, 2)}$$

## Finding Midpoint Quiz

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