MA19.GDA.6
Derive the equation of a circle of given center and radius using the Pythagorean Theorem.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem.
Unpacked Content
UP:MA19.GDA.6
Vocabulary
- Pythagorean theorem
- Radius
- Translation
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)
