Midpoint Formula Color by Number - Free Printable

Let’s solve each problem step by step. We’ll use the midpoint formula:

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

For problems 1–11, we’re given two endpoints and need to find the midpoint. Then we’ll note which coordinate (x or y) to use for coloring.

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

> If midpoint is $(M_x, M_y)$ and one endpoint is $(x_1, y_1)$, then the other endpoint $(x_2, y_2)$ is:
> $x_2 = 2M_x - x_1$
> $y_2 = 2M_y - y_1$

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Problem 1: Endpoints (6, 4), (10, -1)

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

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Problem 2: (5, -8), (3, 4)

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

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Problem 3: (1, -11), (1, -8)

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

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Problem 4: (-3, 4), (-1, -12)

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

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Problem 5: (-1, 7), (-1, -8)

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

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Problem 6: (-1, 9), (5, 9)

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

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Problem 7: (-5, -9), (-4, 8)

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

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Problem 8: (3, -11), (-10, 0)

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

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Problem 9: (4, -10), (2, 2)

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

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Problem 10: (-6, -7), (5, -5)

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

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Problem 11: (14, 0), (-7, 5)

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

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Now problems 12–14: Given one endpoint and midpoint, find the other endpoint.

Formula:
Other endpoint x = 2 × midpoint_x - given_endpoint_x
Other endpoint y = 2 × midpoint_y - given_endpoint_y

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

Other x: 2×8 - (-9) = 16 + 9 = 25
Other y: 2×14 - (-1) = 28 + 1 = 29
→ Other endpoint: (25, 29) → Color Black using x = 25

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Problem 13: Endpoint (10, 12), Midpoint (6, 9)

Other x: 2×6 - 10 = 12 - 10 = 2
Other y: 2×9 - 12 = 18 - 12 = 6
→ Other endpoint: (2, 6) → Color Light blue using x = 2

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Problem 14: Endpoint (-8, -10), Midpoint (10, -7)

Other x: 2×10 - (-8) = 20 + 8 = 28
Other y: 2×(-7) - (-10) = -14 + 10 = -4
→ Other endpoint: (28, -4) → Color Maroon using x = 28

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Final Answer:

1. Midpoint: (8, 1.5) → Light blue (y = 1.5)
2. Midpoint: (4, -2) → Dark blue (x = 4)
3. Midpoint: (1, -9.5) → Maroon (y = -9.5)
4. Midpoint: (-2, -4) → Green (y = -4)
5. Midpoint: (-1, -0.5) → Yellow (x = -1)
6. Midpoint: (2, 9) → Black (y = 9)
7. Midpoint: (-4.5, -0.5) → Light blue (y = -0.5)
8. Midpoint: (-3.5, -5.5) → Dark blue (x = -3.5)
9. Midpoint: (3, -4) → Maroon (x = 3)
10. Midpoint: (-0.5, -6) → Green (y = -6)
11. Midpoint: (3.5, 2.5) → Yellow (x = 3.5)
12. Other endpoint: (25, 29) → Black (x = 25)
13. Other endpoint: (2, 6) → Light blue (x = 2)
14. Other endpoint: (28, -4) → Maroon (x = 28)