MA19.GDA.6

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

Aligned Learning Resources

Determining Surface Area With Unit Blocks

Design by Adaptive Theme