Midpoint Formula worksheet with graphs and coordinate problems.

Let's solve the problem step by step using the midpoint formula.

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🔷 Midpoint Formula

For a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $M$ is given by:

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

We'll apply this formula to each of the problems.

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## ✔ Part 1: Find the midpoint from graphs (Problems 1–4)

Since I can't see the actual images, I will estimate the coordinates of the endpoints based on typical grid representations. If you have specific coordinates, please provide them. But for now, let’s assume standard placements.

However, since the image isn’t visible here, I’ll skip Problems 1–4 unless you can describe the points or confirm their coordinates.

But we can solve Problems 5–14 exactly because they give coordinates.

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## ✔ Part 2: Find the midpoint given endpoints

Let’s compute each one:

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5) $(6, 1), (-2, 5)$

$$
x = \frac{6 + (-2)}{2} = \frac{4}{2} = 2 \\
y = \frac{1 + 5}{2} = \frac{6}{2} = 3 \\
\Rightarrow \boxed{(2, 3)}
$$

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6) $(4, 3), (-1, 6)$

$$
x = \frac{4 + (-1)}{2} = \frac{3}{2} = 1.5 \\
y = \frac{3 + 6}{2} = \frac{9}{2} = 4.5 \\
\Rightarrow \boxed{\left(1.5, 4.5\right)} \text{ or } \boxed{\left(\frac{3}{2}, \frac{9}{2}\right)}
$$

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7) $(-5, 4), (-6, 3)$

$$
x = \frac{-5 + (-6)}{2} = \frac{-11}{2} = -5.5 \\
y = \frac{4 + 3}{2} = \frac{7}{2} = 3.5 \\
\Rightarrow \boxed{(-5.5, 3.5)} \text{ or } \boxed{\left(-\frac{11}{2}, \frac{7}{2}\right)}
$$

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8) $(4, -3), (5, 5)$

$$
x = \frac{4 + 5}{2} = \frac{9}{2} = 4.5 \\
y = \frac{-3 + 5}{2} = \frac{2}{2} = 1 \\
\Rightarrow \boxed{(4.5, 1)} \text{ or } \boxed{\left(\frac{9}{2}, 1\right)}
$$

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9) $(11, -10), (-3, 9)$

$$
x = \frac{11 + (-3)}{2} = \frac{8}{2} = 4 \\
y = \frac{-10 + 9}{2} = \frac{-1}{2} = -0.5 \\
\Rightarrow \boxed{(4, -0.5)} \text{ or } \boxed{\left(4, -\frac{1}{2}\right)}
$$

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10) $(8, 2), (9, 8)$

$$
x = \frac{8 + 9}{2} = \frac{17}{2} = 8.5 \\
y = \frac{2 + 8}{2} = \frac{10}{2} = 5 \\
\Rightarrow \boxed{(8.5, 5)} \text{ or } \boxed{\left(\frac{17}{2}, 5\right)}
$$

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11) $(5, 1), (-4, -12)$

$$
x = \frac{5 + (-4)}{2} = \frac{1}{2} = 0.5 \\
y = \frac{1 + (-12)}{2} = \frac{-11}{2} = -5.5 \\
\Rightarrow \boxed{(0.5, -5.5)} \text{ or } \boxed{\left(\frac{1}{2}, -\frac{11}{2}\right)}
$$

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12) $(-8, -9), (7, 7)$

$$
x = \frac{-8 + 7}{2} = \frac{-1}{2} = -0.5 \\
y = \frac{-9 + 7}{2} = \frac{-2}{2} = -1 \\
\Rightarrow \boxed{(-0.5, -1)} \text{ or } \boxed{\left(-\frac{1}{2}, -1\right)}
$$

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13) $(-9, 8), (0, -11)$

$$
x = \frac{-9 + 0}{2} = \frac{-9}{2} = -4.5 \\
y = \frac{8 + (-11)}{2} = \frac{-3}{2} = -1.5 \\
\Rightarrow \boxed{(-4.5, -1.5)} \text{ or } \boxed{\left(-\frac{9}{2}, -\frac{3}{2}\right)}
$$

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14) $(10, 9), (0, -10)$

$$
x = \frac{10 + 0}{2} = \frac{10}{2} = 5 \\
y = \frac{9 + (-10)}{2} = \frac{-1}{2} = -0.5 \\
\Rightarrow \boxed{(5, -0.5)} \text{ or } \boxed{\left(5, -\frac{1}{2}\right)}
$$

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## ✔ Final Answers:

| Problem | Midpoint |
|--------|----------|
| 5 | $(2, 3)$ |
| 6 | $\left(\frac{3}{2}, \frac{9}{2}\right)$ |
| 7 | $\left(-\frac{11}{2}, \frac{7}{2}\right)$ |
| 8 | $\left(\frac{9}{2}, 1\right)$ |
| 9 | $\left(4, -\frac{1}{2}\right)$ |
| 10 | $\left(\frac{17}{2}, 5\right)$ |
| 11 | $\left(\frac{1}{2}, -\frac{11}{2}\right)$ |
| 12 | $\left(-\frac{1}{2}, -1\right)$ |
| 13 | $\left(-\frac{9}{2}, -\frac{3}{2}\right)$ |
| 14 | $\left(5, -\frac{1}{2}\right)$ |

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If you can describe the endpoints for Problems 1–4 (e.g., "from (-2,1) to (2,5)"), I can help with those too!