If the center of a circle is at (0, 0) and it passes through the point (3, 4), w

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Question: If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the radius of the circle?

Options:

Correct Answer: 5

Solution:

The radius is the distance from the center to the point, which is √(3² + 4²) = √25 = 5.

If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the radius of the circle?

If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the radius of the circle?

Step 1: Identify the center of the circle, which is at the point (0, 0).
Step 2: Identify the point that the circle passes through, which is (3, 4).
Step 3: Use the distance formula to find the radius. The formula is: distance = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates into the formula. Here, (x1, y1) is (0, 0) and (x2, y2) is (3, 4).
Step 5: Calculate the differences: (3 - 0) = 3 and (4 - 0) = 4.
Step 6: Square the differences: 3² = 9 and 4² = 16.
Step 7: Add the squared differences: 9 + 16 = 25.
Step 8: Take the square root of the sum: √25 = 5.
Step 9: The radius of the circle is 5.

Distance Formula – The radius of a circle can be calculated using the distance formula, which is derived from the Pythagorean theorem.