What is the distance between the center of a circle at (2, 3) and a point on the

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Question: What is the distance between the center of a circle at (2, 3) and a point on the circle at (5, 7)?

Options:

Correct Answer: 5

Solution:

Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

What is the distance between the center of a circle at (2, 3) and a point on the circle at (5, 7)?

What is the distance between the center of a circle at (2, 3) and a point on the circle at (5, 7)?

Step 1: Identify the center of the circle, which is at the point (2, 3).
Step 2: Identify the point on the circle, which is at the point (5, 7).
Step 3: Use the distance formula, which is Distance = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates into the formula: x1 = 2, y1 = 3, x2 = 5, y2 = 7.
Step 5: Calculate (x2 - x1): 5 - 2 = 3.
Step 6: Calculate (y2 - y1): 7 - 3 = 4.
Step 7: Square the results: (3)² = 9 and (4)² = 16.
Step 8: Add the squared results: 9 + 16 = 25.
Step 9: Take the square root of the sum: √25 = 5.
Step 10: The distance between the center of the circle and the point on the circle is 5.

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