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 formula in reverse:

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

$$
x_2 = 2M_x - x_1,\quad y_2 = 2M_y - y_1
$$

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## ✔ Part 1: Find the Midpoint

1. $ (6, 4), (10, -1) $

$$
x = \frac{6 + 10}{2} = \frac{16}{2} = 8,\quad y = \frac{4 + (-1)}{2} = \frac{3}{2} = 1.5
$$
Midpoint: $ (8, 1.5) $ → Light blue (y) → color y = 1.5

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2. $ (5, -8), (3, 4) $

$$
x = \frac{5 + 3}{2} = 4,\quad y = \frac{-8 + 4}{2} = \frac{-4}{2} = -2
$$
Midpoint: $ (4, -2) $ → Dark blue (x) → color x = 4

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3. $ (1, -11), (1, -8) $

$$
x = \frac{1 + 1}{2} = 1,\quad y = \frac{-11 + (-8)}{2} = \frac{-19}{2} = -9.5
$$
Midpoint: $ (1, -9.5) $ → Maroon (y) → color y = -9.5

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4. $ (-3, 4), (-1, -12) $

$$
x = \frac{-3 + (-1)}{2} = \frac{-4}{2} = -2,\quad y = \frac{4 + (-12)}{2} = \frac{-8}{2} = -4
$$
Midpoint: $ (-2, -4) $ → Green (y) → color y = -4

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5. $ (-1, 7), (-1, -8) $

$$
x = \frac{-1 + (-1)}{2} = -1,\quad y = \frac{7 + (-8)}{2} = \frac{-1}{2} = -0.5
$$
Midpoint: $ (-1, -0.5) $ → Yellow (x) → color x = -1

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6. $ (-1, 9), (5, 9) $

$$
x = \frac{-1 + 5}{2} = \frac{4}{2} = 2,\quad y = \frac{9 + 9}{2} = 9
$$
Midpoint: $ (2, 9) $ → Black (y) → color y = 9

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7. $ (-5, -9), (-4, 8) $

$$
x = \frac{-5 + (-4)}{2} = \frac{-9}{2} = -4.5,\quad y = \frac{-9 + 8}{2} = \frac{-1}{2} = -0.5
$$
Midpoint: $ (-4.5, -0.5) $ → Light blue (y) → color y = -0.5

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8. $ (3, -11), (-10, 0) $

$$
x = \frac{3 + (-10)}{2} = \frac{-7}{2} = -3.5,\quad y = \frac{-11 + 0}{2} = \frac{-11}{2} = -5.5
$$
Midpoint: $ (-3.5, -5.5) $ → Dark blue (x) → color x = -3.5

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9. $ (4, -10), (2, 2) $

$$
x = \frac{4 + 2}{2} = 3,\quad y = \frac{-10 + 2}{2} = \frac{-8}{2} = -4
$$
Midpoint: $ (3, -4) $ → Maroon (x) → color x = 3

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10. $ (-6, -7), (5, -5) $

$$
x = \frac{-6 + 5}{2} = \frac{-1}{2} = -0.5,\quad y = \frac{-7 + (-5)}{2} = \frac{-12}{2} = -6
$$
Midpoint: $ (-0.5, -6) $ → Green (y) → color y = -6

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11. $ (14, 0), (-7, 5) $

$$
x = \frac{14 + (-7)}{2} = \frac{7}{2} = 3.5,\quad y = \frac{0 + 5}{2} = 2.5
$$
Midpoint: $ (3.5, 2.5) $ → Yellow (x) → color x = 3.5

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## ✔ Part 2: Find the Other Endpoint

We use:
$$
\text{Other endpoint} = (2M_x - x_1, 2M_y - y_1)
$$

12. Endpoint: $ (-9, -1) $, Midpoint: $ (8, 14) $

$$
x = 2(8) - (-9) = 16 + 9 = 25 \\
y = 2(14) - (-1) = 28 + 1 = 29
$$
Other endpoint: $ (25, 29) $ → Black (x) → color x = 25

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13. Endpoint: $ (10, 12) $, Midpoint: $ (6, 9) $

$$
x = 2(6) - 10 = 12 - 10 = 2 \\
y = 2(9) - 12 = 18 - 12 = 6
$$
Other endpoint: $ (2, 6) $ → Light blue (x) → color x = 2

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14. Endpoint: $ (-8, -10) $, Midpoint: $ (10, -7) $

$$
x = 2(10) - (-8) = 20 + 8 = 28 \\
y = 2(-7) - (-10) = -14 + 10 = -4
$$
Other endpoint: $ (28, -4) $ → Maroon (x) → color x = 28

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## ✔ Final Answers Summary:

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

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🎨 Coloring Instructions (for Mandala):

You would now go to your mandala and:

- Color the y-coordinate = 1.5 with light blue
- Color x = 4 with dark blue
- Color y = -9.5 with maroon
- Color y = -4 with green
- Color x = -1 with yellow
- Color y = 9 with black
- Color y = -0.5 with light blue
- Color x = -3.5 with dark blue
- Color x = 3 with maroon
- Color y = -6 with green
- Color x = 3.5 with yellow
- Color x = 25 with black
- Color x = 2 with light blue
- Color x = 28 with maroon

> ⚠️ Note: The mandala likely has coordinate points labeled. You’ll need to locate each coordinate value (like x=4 or y=-2) on the mandala and fill in the corresponding section with the assigned color.

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✔ All problems solved!
Let me know if you'd like a printable version or help coloring the mandala.