Question

Cameron: (70, 40)
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Part 1
​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.
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Part 1
Arthur is about
  
enter your response here meters away from​ Cameron, and Jamie is about
  
enter your response here meters away from​ Cameron, so
▼
is closer to Cameron.
​(Round to the nearest whole number as​ needed.)
Arthur: (20, 50)

Jamie: (40, 30)

Answer 1

To determine who is closer to Cameron, we need to calculate the distance between Cameron and each of the players, Arthur and Jamie, using the distance formula. The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

### Step 1: Calculate the distance from Cameron to Arthur.

- Cameron's coordinates: \( (70, 40) \)
- Arthur's coordinates: \( (20, 50) \)

Using the distance formula:

\[
d_{CA} = \sqrt{(20 - 70)^2 + (50 - 40)^2}
\]
\[
d_{CA} = \sqrt{(-50)^2 + (10)^2}
\]
\[
d_{CA} = \sqrt{2500 + 100}
\]
\[
d_{CA} = \sqrt{2600}
\]
\[
d_{CA} \approx 50.99 \text{ meters} \quad \text{(rounds to 51)}
\]

### Step 2: Calculate the distance from Cameron to Jamie.

- Jamie's coordinates: \( (40, 30) \)

Using the distance formula:

\[
d_{CJ} = \sqrt{(40 - 70)^2 + (30 - 40)^2}
\]
\[
d_{CJ} = \sqrt{(-30)^2 + (-10)^2}
\]
\[
d_{CJ} = \sqrt{900 + 100}
\]
\[
d_{CJ} = \sqrt{1000}
\]
\[
d_{CJ} \approx 31.62 \text{ meters} \quad \text{(rounds to 32)}
\]

### Conclusion:

- Arthur is about **51** meters away from Cameron.
- Jamie is about **32** meters away from Cameron.

So, **Jamie is closer to Cameron**.

### Final response:
Arthur is about 51 meters away from Cameron, and Jamie is about 32 meters away from Cameron, so Jamie is closer to Cameron.