Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.6

Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

Unpacked Content

Knowledge

Students know:
  • Key features of a circle.
  • The Pythagorean Theorem, Midpoint Formula, Distance Formula.

Skills

Students are able to:
  • Create a right triangle in a circle using the horizontal and vertical shifts from the center as the legs and the radius of the circle as the hypotenuse.
  • Write the equation of the circle in standard form when given the endpoints of the diameter of a circle, using the midpoint formula to find the circle's center, and then use the Pythagorean Theorem to find the equation of the circle.
  • Find the distance between two points when using the Pythagorean Theorem and use that process to create the Distance Formula.

Understanding

Students understand that:
  • Circles represent a fixed distance in all directions in a plane from a given point, and a right triangle may be created to show the relationship of the horizontal and vertical shift to the distance,
  • Circles written in standard form are useful for recognizing the center and radius of a circle.
  • The distance formula and Pythagorean Theorem can both be used to find length measurements of segments (or sides of a geometric figure)

Vocabulary

  • Pythagorean theorem
  • Radius
  • Translation
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