Finding the Center and Radius of a circle

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SUMMARY

The center of a circle defined by the endpoints of its diameter at (-9, -6) and (-1, 0) is calculated as the midpoint, resulting in the coordinates (-5, -3). This is derived using the formula for the midpoint, which averages the x-coordinates and y-coordinates of the endpoints. The radius of the circle is determined by measuring the distance from the center (-5, -3) to either endpoint, which can be calculated using the distance formula.

PREREQUISITES
  • Understanding of coordinate geometry
  • Familiarity with the midpoint formula
  • Knowledge of the distance formula
  • Basic algebra skills
NEXT STEPS
  • Review the derivation of the midpoint formula in coordinate geometry
  • Practice calculating the distance between two points using the distance formula
  • Explore the properties of circles in geometry
  • Learn how to graph circles given their center and radius
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Students studying geometry, educators teaching coordinate systems, and anyone interested in understanding the properties of circles.

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What is the center and radius of a circle that has a diameter with endpoints (-9,-6) and (-1,0)
 
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That's very close to being trivial! The center of the circle is at the midpoint of any diameter. And the midpoint of the line segment between two points is the average of the two points. The center of the circle is the midpoint of the line between (-9, -6) and (-1, 0): ((-9+(-1))/2, (-6+0)/2)= (-10/2, -6/2)= (-5, -3). And the radius is the distance from (-5, -3) to either of the given points.
 

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