Midpoint Formula Color by Number - Free Printable

Let's solve this Midpoint Formula Color by Number worksheet step by step.

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🔷 Midpoint Formula:

The midpoint $ M $ of a line segment with endpoints $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

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

For problems 12–14, we are given one endpoint and the midpoint, and we need to find the other endpoint. We can use the reverse of the midpoint formula:

If:
- Endpoint: $ (x_1, y_1) $
- Midpoint: $ (m_x, m_y) $
- Unknown endpoint: $ (x_2, y_2) $

Then:
$$
m_x = \frac{x_1 + x_2}{2} \Rightarrow x_2 = 2m_x - x_1
$$
$$
m_y = \frac{y_1 + y_2}{2} \Rightarrow y_2 = 2m_y - y_1
$$

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✔ Part 1: Find the Midpoint

#### 1. $ (6, 4), (10, -1) $
$$
\left( \frac{6+10}{2}, \frac{4+(-1)}{2} \right) = \left( \frac{16}{2}, \frac{3}{2} \right) = (8, 1.5)
$$
✔ Midpoint: $ (8, 1.5) $ → Color: Light blue (y) → Use y = 1.5

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#### 2. $ (5, -8), (3, 4) $
$$
\left( \frac{5+3}{2}, \frac{-8+4}{2} \right) = \left( \frac{8}{2}, \frac{-4}{2} \right) = (4, -2)
$$
✔ Midpoint: $ (4, -2) $ → Color: Dark blue (x) → Use x = 4

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#### 3. $ (1, -11), (1, -8) $
$$
\left( \frac{1+1}{2}, \frac{-11 + (-8)}{2} \right) = \left( \frac{2}{2}, \frac{-19}{2} \right) = (1, -9.5)
$$
✔ Midpoint: $ (1, -9.5) $ → Color: Maroon (y) → Use y = -9.5

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#### 4. $ (-3, 4), (-1, -12) $
$$
\left( \frac{-3 + (-1)}{2}, \frac{4 + (-12)}{2} \right) = \left( \frac{-4}{2}, \frac{-8}{2} \right) = (-2, -4)
$$
✔ Midpoint: $ (-2, -4) $ → Color: Green (y) → Use y = -4

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#### 5. $ (-1, 7), (-1, -8) $
$$
\left( \frac{-1 + (-1)}{2}, \frac{7 + (-8)}{2} \right) = \left( \frac{-2}{2}, \frac{-1}{2} \right) = (-1, -0.5)
$$
✔ Midpoint: $ (-1, -0.5) $ → Color: Yellow (x) → Use x = -1

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#### 6. $ (-1, 9), (5, 9) $
$$
\left( \frac{-1 + 5}{2}, \frac{9 + 9}{2} \right) = \left( \frac{4}{2}, \frac{18}{2} \right) = (2, 9)
$$
✔ Midpoint: $ (2, 9) $ → Color: Black (y) → Use y = 9

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#### 7. $ (-5, -9), (-4, 8) $
$$
\left( \frac{-5 + (-4)}{2}, \frac{-9 + 8}{2} \right) = \left( \frac{-9}{2}, \frac{-1}{2} \right) = (-4.5, -0.5)
$$
✔ Midpoint: $ (-4.5, -0.5) $ → Color: Light blue (y) → Use y = -0.5

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#### 8. $ (3, -11), (-10, 0) $
$$
\left( \frac{3 + (-10)}{2}, \frac{-11 + 0}{2} \right) = \left( \frac{-7}{2}, \frac{-11}{2} \right) = (-3.5, -5.5)
$$
✔ Midpoint: $ (-3.5, -5.5) $ → Color: Dark blue (x) → Use x = -3.5

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#### 9. $ (4, -10), (2, 2) $
$$
\left( \frac{4 + 2}{2}, \frac{-10 + 2}{2} \right) = \left( \frac{6}{2}, \frac{-8}{2} \right) = (3, -4)
$$
✔ Midpoint: $ (3, -4) $ → Color: Maroon (x) → Use x = 3

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#### 10. $ (-6, -7), (5, -5) $
$$
\left( \frac{-6 + 5}{2}, \frac{-7 + (-5)}{2} \right) = \left( \frac{-1}{2}, \frac{-12}{2} \right) = (-0.5, -6)
$$
✔ Midpoint: $ (-0.5, -6) $ → Color: Green (y) → Use y = -6

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#### 11. $ (14, 0), (-7, 5) $
$$
\left( \frac{14 + (-7)}{2}, \frac{0 + 5}{2} \right) = \left( \frac{7}{2}, \frac{5}{2} \right) = (3.5, 2.5)
$$
✔ Midpoint: $ (3.5, 2.5) $ → Color: Yellow (x) → Use x = 3.5

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✔ Part 2: Given Midpoint and One Endpoint, Find Other Endpoint

Use:
$$
x_2 = 2m_x - x_1,\quad y_2 = 2m_y - y_1
$$

#### 12. Endpoint: $ (-9, -1) $, Midpoint: $ (8, 14) $
$$
x_2 = 2(8) - (-9) = 16 + 9 = 25 \\
y_2 = 2(14) - (-1) = 28 + 1 = 29
$$
✔ Other endpoint: $ (25, 29) $ → Color: Black (x) → Use x = 25

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#### 13. Endpoint: $ (10, 12) $, Midpoint: $ (6, 9) $
$$
x_2 = 2(6) - 10 = 12 - 10 = 2 \\
y_2 = 2(9) - 12 = 18 - 12 = 6
$$
✔ Other endpoint: $ (2, 6) $ → Color: Light blue (x) → Use x = 2

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#### 14. Endpoint: $ (-8, -10) $, Midpoint: $ (10, -7) $
$$
x_2 = 2(10) - (-8) = 20 + 8 = 28 \\
y_2 = 2(-7) - (-10) = -14 + 10 = -4
$$
✔ Other endpoint: $ (28, -4) $ → Color: Maroon (x) → Use x = 28

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🎨 Final Answers Summary:

| Problem | Midpoint / Other Endpoint | Coordinate Used | Color |
|--------|----------------------------|------------------|-------|
| 1 | (8, 1.5) | y = 1.5 | Light blue |
| 2 | (4, -2) | x = 4 | Dark blue |
| 3 | (1, -9.5) | y = -9.5 | Maroon |
| 4 | (-2, -4) | y = -4 | Green |
| 5 | (-1, -0.5) | x = -1 | Yellow |
| 6 | (2, 9) | y = 9 | Black |
| 7 | (-4.5, -0.5) | y = -0.5 | Light blue |
| 8 | (-3.5, -5.5) | x = -3.5 | Dark blue |
| 9 | (3, -4) | x = 3 | Maroon |
| 10 | (-0.5, -6) | y = -6 | Green |
| 11 | (3.5, 2.5) | x = 3.5 | Yellow |
| 12 | (25, 29) | x = 25 | Black |
| 13 | (2, 6) | x = 2 | Light blue |
| 14 | (28, -4) | x = 28 | Maroon |

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📝 Instructions for Coloring:

You would now:
- On a mandala (not shown here), locate the coordinate (x or y) as specified.
- Color that specific coordinate point using the indicated color.

> Example: For problem 1, you would go to y = 1.5 on the mandala and color it light blue.

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✔ All problems solved! You're ready to color your mandala based on these results.

Let me know if you'd like a printable version or help coloring!