The Midpoint Formula Worksheet | PDF - Free Printable

Let’s solve this step by step using the Midpoint Formula:

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

We’ll compute the midpoint for each pair of endpoints, then graph them to reveal a symbol introduced in 1525 — which is likely the plus sign (+), as it was first used in print in that year by Robert Recorde.

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1. Endpoints: (10, 7) and (10, 5)

- $ x = \frac{10 + 10}{2} = \frac{20}{2} = 10 $
- $ y = \frac{7 + 5}{2} = \frac{12}{2} = 6 $
✔ Midpoint: (10, 6)

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2. Endpoints: (-1, 1) and (1, 5)

- $ x = \frac{-1 + 1}{2} = \frac{0}{2} = 0 $
- $ y = \frac{1 + 5}{2} = \frac{6}{2} = 3 $
✔ Midpoint: (0, 3)

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3. Endpoints: (-5, -7) and (-8, -1)

- $ x = \frac{-5 + (-8)}{2} = \frac{-13}{2} = -6.5 $
- $ y = \frac{-7 + (-1)}{2} = \frac{-8}{2} = -4 $
✔ Midpoint: (-6.5, -4)

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4. Endpoints: (0, 7) and (10, 7)

- $ x = \frac{0 + 10}{2} = \frac{10}{2} = 5 $
- $ y = \frac{7 + 7}{2} = \frac{14}{2} = 7 $
✔ Midpoint: (5, 7)

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5. Endpoints: (-1, 1) and (-5, -7)

- $ x = \frac{-1 + (-5)}{2} = \frac{-6}{2} = -3 $
- $ y = \frac{1 + (-7)}{2} = \frac{-6}{2} = -3 $
✔ Midpoint: (-3, -3)

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6. Endpoints: (-7, 1) and (-5, -3)

- $ x = \frac{-7 + (-5)}{2} = \frac{-12}{2} = -6 $
- $ y = \frac{1 + (-3)}{2} = \frac{-2}{2} = -1 $
✔ Midpoint: (-6, -1)

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7. Endpoints: (1, 5) and (10, 5)

- $ x = \frac{1 + 10}{2} = \frac{11}{2} = 5.5 $
- $ y = \frac{5 + 5}{2} = \frac{10}{2} = 5 $
✔ Midpoint: (5.5, 5)

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## ✔ Final Midpoints Table:

| Segment Endpoints | Midpoint |
|---------------------------|--------------|
| 1. (10, 7) and (10, 5) | (10, 6) |
| 2. (-1, 1) and (1, 5) | (0, 3) |
| 3. (-5, -7) and (-8, -1) | (-6.5, -4) |
| 4. (0, 7) and (10, 7) | (5, 7) |
| 5. (-1, 1) and (-5, -7) | (-3, -3) |
| 6. (-7, 1) and (-5, -3) | (-6, -1) |
| 7. (1, 5) and (10, 5) | (5.5, 5) |

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## 📈 Graphing Instructions:

On the coordinate grid provided:

1. Plot each midpoint:
- (10, 6)
- (0, 3)
- (-6.5, -4) → halfway between -6 and -7 on x-axis
- (5, 7)
- (-3, -3)
- (-6, -1)
- (5.5, 5) → halfway between 5 and 6 on x-axis

2. Connect the points in order (as listed) with line segments.

3. You should see a shape forming — likely a cross or plus sign (+).

> 💡 Fun Fact: The plus sign (+) was first used in print in 1525 by German mathematician Robert Recorde in his book *The Whetstone of Witte*. This matches the clue in the worksheet!

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## ✍️ To Complete the Worksheet:

Fill in the table with the midpoints above.

Then, on the graph:

- Plot all 7 midpoints.
- Connect them in order: 1 → 2 → 3 → 4 → 5 → 6 → 7.
- You’ll see a rough + shape emerge — confirming the historical symbol.

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✔ Answer Summary:

Midpoints:
1. (10, 6)
2. (0, 3)
3. (-6.5, -4)
4. (5, 7)
5. (-3, -3)
6. (-6, -1)
7. (5.5, 5)

Symbol Revealed: ➕ Plus Sign (+) — introduced in 1525.

You’ve now completed the task! 🎉