Midpoint of a Line Segment Worksheets - Free Printable

To solve the problem of finding the midpoint of each line segment, we will use the Midpoint Formula. The formula for the midpoint \( M \) of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Step-by-Step Solution for Each Line Segment

#### 1)
- Endpoints: \( A(-2, 3) \) and \( B(4, -1) \)
- Using the midpoint formula:
\[
M = \left( \frac{-2 + 4}{2}, \frac{3 + (-1)}{2} \right) = \left( \frac{2}{2}, \frac{2}{2} \right) = (1, 1)
\]
- Midpoint: \( (1, 1) \)

#### 2)
- Endpoints: \( A(0, 5) \) and \( B(6, 1) \)
- Using the midpoint formula:
\[
M = \left( \frac{0 + 6}{2}, \frac{5 + 1}{2} \right) = \left( \frac{6}{2}, \frac{6}{2} \right) = (3, 3)
\]
- Midpoint: \( (3, 3) \)

#### 3)
- Endpoints: \( A(-3, 4) \) and \( B(5, -2) \)
- Using the midpoint formula:
\[
M = \left( \frac{-3 + 5}{2}, \frac{4 + (-2)}{2} \right) = \left( \frac{2}{2}, \frac{2}{2} \right) = (1, 1)
\]
- Midpoint: \( (1, 1) \)

#### 4)
- Endpoints: \( A(-4, 0) \) and \( B(2, 0) \)
- Using the midpoint formula:
\[
M = \left( \frac{-4 + 2}{2}, \frac{0 + 0}{2} \right) = \left( \frac{-2}{2}, \frac{0}{2} \right) = (-1, 0)
\]
- Midpoint: \( (-1, 0) \)

#### 5)
- Endpoints: \( A(1, 4) \) and \( B(5, 2) \)
- Using the midpoint formula:
\[
M = \left( \frac{1 + 5}{2}, \frac{4 + 2}{2} \right) = \left( \frac{6}{2}, \frac{6}{2} \right) = (3, 3)
\]
- Midpoint: \( (3, 3) \)

#### 6)
- Endpoints: \( A(0, 0) \) and \( B(6, 6) \)
- Using the midpoint formula:
\[
M = \left( \frac{0 + 6}{2}, \frac{0 + 6}{2} \right) = \left( \frac{6}{2}, \frac{6}{2} \right) = (3, 3)
\]
- Midpoint: \( (3, 3) \)

#### 7)
- Endpoints: \( A(-1, 2) \) and \( B(3, -2) \)
- Using the midpoint formula:
\[
M = \left( \frac{-1 + 3}{2}, \frac{2 + (-2)}{2} \right) = \left( \frac{2}{2}, \frac{0}{2} \right) = (1, 0)
\]
- Midpoint: \( (1, 0) \)

#### 8)
- Endpoints: \( A(2, -3) \) and \( B(4, 1) \)
- Using the midpoint formula:
\[
M = \left( \frac{2 + 4}{2}, \frac{-3 + 1}{2} \right) = \left( \frac{6}{2}, \frac{-2}{2} \right) = (3, -1)
\]
- Midpoint: \( (3, -1) \)

#### 9)
- Endpoints: \( A(1, 3) \) and \( B(5, -1) \)
- Using the midpoint formula:
\[
M = \left( \frac{1 + 5}{2}, \frac{3 + (-1)}{2} \right) = \left( \frac{6}{2}, \frac{2}{2} \right) = (3, 1)
\]
- Midpoint: \( (3, 1) \)

Final Answer

\[
\boxed{
\begin{array}{ll}
1) & (1, 1) \\
2) & (3, 3) \\
3) & (1, 1) \\
4) & (-1, 0) \\
5) & (3, 3) \\
6) & (3, 3) \\
7) & (1, 0) \\
8) & (3, -1) \\
9) & (3, 1) \\
\end{array}
}
\]