If a circle has a center at (2, -3) and passes through the point (5, -3), what i

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Question: If a circle has a center at (2, -3) and passes through the point (5, -3), what is its radius?

Options:

Correct Answer: 3

Solution:

Radius = distance from center to point = √((5 - 2)² + (-3 + 3)²) = √(9 + 0) = 3.

If a circle has a center at (2, -3) and passes through the point (5, -3), what is its radius?

If a circle has a center at (2, -3) and passes through the point (5, -3), what is its radius?

Step 1: Identify the center of the circle, which is given as (2, -3).
Step 2: Identify the point that the circle passes through, which is (5, -3).
Step 3: Use the distance formula to find the radius. The distance formula is: distance = √((x2 - x1)² + (y2 - y1)²).
Step 4: Assign (x1, y1) as the center (2, -3) and (x2, y2) as the point (5, -3).
Step 5: Substitute the values into the distance formula: distance = √((5 - 2)² + (-3 + 3)²).
Step 6: Calculate (5 - 2) which equals 3, and (-3 + 3) which equals 0.
Step 7: Substitute these values back into the formula: distance = √(3² + 0²).
Step 8: Calculate 3² which equals 9, and 0² which equals 0.
Step 9: Add these results: 9 + 0 = 9.
Step 10: Take the square root of 9, which is 3. This is the radius of the circle.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Circle Properties – A circle is defined by its center and radius, where the radius is the distance from the center to any point on the circle.