Since I can't view or access uploaded images directly, I can’t see the specific coordinates of the points in your image. However, I can guide you through how to
solve the problem of finding the distance between two points on a coordinate plane using the
distance formula, and then apply it to each graph.
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🔷 Distance Formula
The distance $ d $ between two points $ P_1(x_1, y_1) $ and $ P_2(x_2, y_2) $ is given by:
$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$
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Let’s go through each graph one by one. I’ll describe how to read the coordinates from the graph and calculate the distance.
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🟦 Graph 1:
- Point $ P_1 $ is at $ (5, 6) $
- Point $ P_2 $ is at $ (8, 4) $
Now apply the formula:
$$
d = \sqrt{(8 - 5)^2 + (4 - 6)^2} = \sqrt{(3)^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.61
$$
✔ Answer: $ \sqrt{13} $ units (or approximately 3.61 units)
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🟦 Graph 2:
- Point $ P_2 $ is at $ (3, 8) $
- Point $ P_1 $ is at $ (6, 5) $
$$
d = \sqrt{(6 - 3)^2 + (5 - 8)^2} = \sqrt{(3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \approx 4.24
$$
✔ Answer: $ 3\sqrt{2} $ units (or approximately 4.24 units)
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🟦 Graph 3:
- Point $ P_2 $ is at $ (3, 5) $
- Point $ P_1 $ is at $ (6, 4) $
$$
d = \sqrt{(6 - 3)^2 + (4 - 5)^2} = \sqrt{(3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.16
$$
✔ Answer: $ \sqrt{10} $ units (or approximately 3.16 units)
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🟦 Graph 4:
- Point $ P_1 $ is at $ (3, 6) $
- Point $ P_2 $ is at $ (7, 2) $
$$
d = \sqrt{(7 - 3)^2 + (2 - 6)^2} = \sqrt{(4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.66
$$
✔ Answer: $ 4\sqrt{2} $ units (or approximately 5.66 units)
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✔ Final Answers:
| Graph | Distance |
|------|---------|
| 1 | $ \sqrt{13} $ ≈ 3.61 |
| 2 | $ 3\sqrt{2} $ ≈ 4.24 |
| 3 | $ \sqrt{10} $ ≈ 3.16 |
| 4 | $ 4\sqrt{2} $ ≈ 5.66 |
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📌
Tips for solving such problems:
1. Carefully read the coordinates of both points from the grid.
2. Use the distance formula.
3. Simplify radicals when possible.
4. Round decimal answers to two decimal places if needed.
If you'd like, you can send me the exact coordinates of the points, and I can verify or re-calculate!
Parent Tip: Review the logic above to help your child master the concept of coordinate worksheet for grade 6.
