If the center of a circle is at (3, 4) and it passes through the point (7, 1), w

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Question: If the center of a circle is at (3, 4) and it passes through the point (7, 1), what is the radius? (2019)

Options:

Correct Answer: 5 units

Exam Year: 2019

Solution:

Radius = distance from center to point = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.

If the center of a circle is at (3, 4) and it passes through the point (7, 1), what is the radius? (2019)

If the center of a circle is at (3, 4) and it passes through the point (7, 1), what is the radius? (2019)

Step 1: Identify the center of the circle, which is at the point (3, 4).
Step 2: Identify the point that the circle passes through, which is (7, 1).
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 (3, 4) and (x2, y2) is (7, 1).
Step 5: Calculate (x2 - x1), which is (7 - 3) = 4.
Step 6: Calculate (y2 - y1), which is (1 - 4) = -3.
Step 7: Square the results from Step 5 and Step 6. So, (4)² = 16 and (-3)² = 9.
Step 8: Add the squared results together: 16 + 9 = 25.
Step 9: Take the square root of the sum from Step 8: √25 = 5.
Step 10: The radius of the circle is 5 units.

Distance Formula – The radius of a circle can be calculated using the distance formula between two points in a Cartesian plane.
Circle Properties – Understanding the definition of a circle, where the radius is the distance from the center to any point on the circle.