Cameron, Arthur, and Jamie are playing soccer. Their locations are recorded by a motion tracking system. The grid shows distances in meters. Who is closer to​ Cameron? Explain Aruthor is at (20,35) Jamie is (45,15) cameron is at (70,45)

To determine who is closer to Cameron, we need to calculate the distance between Cameron and both Arthur and Jamie using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points.

### Step 1: Distance between Cameron and Arthur

Arthur's coordinates are \((20, 35)\) and Cameron's coordinates are \((70, 45)\).

\[
d_{\text{Cameron, Arthur}} = \sqrt{(70 - 20)^2 + (45 - 35)^2} = \sqrt{50^2 + 10^2} = \sqrt{2500 + 100} = \sqrt{2600} \approx 50.99
\]

### Step 2: Distance between Cameron and Jamie

Jamie's coordinates are \((45, 15)\) and Cameron's coordinates are \((70, 45)\).

\[
d_{\text{Cameron, Jamie}} = \sqrt{(70 - 45)^2 + (45 - 15)^2} = \sqrt{25^2 + 30^2} = \sqrt{625 + 900} = \sqrt{1525} \approx 39.05
\]

### Conclusion:

- The distance between Cameron and Arthur is approximately 50.99 meters.
- The distance between Cameron and Jamie is approximately 39.05 meters.

Thus, **Jamie is closer to Cameron** than Arthur.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How does the distance formula relate to the Pythagorean theorem?
2. If all three players moved simultaneously, how would their new distances change?
3. Can you find the midpoint between Cameron and Jamie?
4. What if we added another player? How would we compare distances between four players?
5. How would this problem change if we considered three-dimensional space?

**Tip:** The distance formula is a direct application of the Pythagorean theorem in two dimensions.

Cameron, Arthur, and Jamie are playing soccer. Their locations are recorded by a motion tracking system. The grid shows distances in meters. Who is closer to Cameron? Arthur is at (20,35), Jamie is at (45,15), Cameron is at (70,45).

Explore how to determine which soccer player is closer to Cameron by applying the distance formula. Arthur is at (20,35), Jamie is at (45,15), and Cameron is at (70,45). Using the Pythagorean theorem, we calculate that Jamie is closer. Suitable for Grades 8-10.

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