If the coordinates of the center of a circle are (4, -2) and it passes through t

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Question: If the coordinates of the center of a circle are (4, -2) and it passes through the point (4, 2), what is the radius of the circle?

Options:

Correct Answer: 2

Solution:

Using the distance formula: radius = √((4 - 4)² + (2 - (-2))²) = √(0 + 16) = √16 = 4.

If the coordinates of the center of a circle are (4, -2) and it passes through the point (4, 2), what is the radius of the circle?

If the coordinates of the center of a circle are (4, -2) and it passes through the point (4, 2), what is the radius of the circle?

Step 1: Identify the center of the circle, which is given as (4, -2).
Step 2: Identify the point that the circle passes through, which is (4, 2).
Step 3: Use the distance formula to find the radius. The distance formula is: radius = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates into the formula. Here, (x1, y1) is (4, -2) and (x2, y2) is (4, 2).
Step 5: Calculate the difference in the x-coordinates: (4 - 4) = 0.
Step 6: Calculate the difference in the y-coordinates: (2 - (-2)) = 2 + 2 = 4.
Step 7: Square the differences: (0)² = 0 and (4)² = 16.
Step 8: Add the squared differences: 0 + 16 = 16.
Step 9: Take the square root of the sum: √16 = 4.
Step 10: The radius of the circle is 4.

Distance Formula – The distance formula is used to calculate the distance between two points in a Cartesian plane, which is essential for determining the radius of a circle given its center and a point on the circle.
Circle Properties – Understanding the properties of a circle, including the definition of radius as the distance from the center to any point on the circle.