Geometry and TrigonometryMediumRadius from the centre and a point on the circle
Geometry and Trigonometry practice question
In the xy-plane, a circle has centre (2, −1) and passes through the point (5, 3). What is the radius of the circle?
Answer: 5
The radius is the distance from the centre to the point: √((5 − 2)² + (3 − (−1))²) = √(9 + 16) = √25 = 5.
Common wrong answers
- If you answered 7
- 7 is 3 + 4, adding the horizontal and vertical distances instead of using the Pythagorean theorem.
- If you answered 25
- 25 is r², the sum of the squares; take the square root.
- If you answered 3.6
- 3.6 is about √(9 + 4), using 3 − 1 = 2 for the vertical change instead of 3 − (−1) = 4.
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