To solve this problem, we will use the
Midpoint Formula. The midpoint $ M $ of two points $ (x_1, y_1) $ and $ (x_2, y_2) $ 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 pair of points.
---
1. $ (3, 8), (9, 2) $
$$
x = \frac{3 + 9}{2} = \frac{12}{2} = 6 \\
y = \frac{8 + 2}{2} = \frac{10}{2} = 5
$$
✔ Midpoint: $ (6, 5) $
---
2. $ (5, 6), (4, 8) $
$$
x = \frac{5 + 4}{2} = \frac{9}{2} = 4.5 \\
y = \frac{6 + 8}{2} = \frac{14}{2} = 7
$$
✔ Midpoint: $ (4.5, 7) $
---
3. $ (2, 3), (5, 7) $
$$
x = \frac{2 + 5}{2} = \frac{7}{2} = 3.5 \\
y = \frac{3 + 7}{2} = \frac{10}{2} = 5
$$
✔ Midpoint: $ (3.5, 5) $
---
4. $ (5, 4), (6, 3) $
$$
x = \frac{5 + 6}{2} = \frac{11}{2} = 5.5 \\
y = \frac{4 + 3}{2} = \frac{7}{2} = 3.5
$$
✔ Midpoint: $ (5.5, 3.5) $
---
5. $ (9, 3), (7, 1) $
$$
x = \frac{9 + 7}{2} = \frac{16}{2} = 8 \\
y = \frac{3 + 1}{2} = \frac{4}{2} = 2
$$
✔ Midpoint: $ (8, 2) $
---
6. $ (3, 6), (9, 1) $
$$
x = \frac{3 + 9}{2} = \frac{12}{2} = 6 \\
y = \frac{6 + 1}{2} = \frac{7}{2} = 3.5
$$
✔ Midpoint: $ (6, 3.5) $
---
✔ Final Answers:
| Points | Midpoint |
|--------|----------|
| (3,8), (9,2) | (6, 5) |
| (5,6), (4,8) | (4.5, 7) |
| (2,3), (5,7) | (3.5, 5) |
| (5,4), (6,3) | (5.5, 3.5) |
| (9,3), (7,1) | (8, 2) |
| (3,6), (9,1) | (6, 3.5) |
Let me know if you'd like these written as fractions instead of decimals!
Parent Tip: Review the logic above to help your child master the concept of midpoint formula worksheet.
