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# G-C-1-4

last edited by 3 years, 8 months ago

G.C.1.4 Apply the distance and midpoint formula, where appropriate, to develop the equation of a circle in standard form.

In a Nutshell

Students will learn to write the equation of a circle when given the center of the circle and a point on the circle.  Students will apply the knowledge of the distance formula to find the value for the radius.

## Teacher Actions

• Develop a deep and flexible conceptual understanding: Students will develop a deep and flexible conceptual understanding of circles by applying and extending their previous knowledge of the distance and midpoint formula to find unknown measurements within a circle.

• Develop accurate and appropriate procedural fluency: Students will develop accurate and appropriate procedural fluency by understanding that the distance formula is used to find the length of the radius and the midpoint formula is used to find the center of the circle.
• Teachers will build procedural fluency from conceptual understanding by showing the relationship between the use of the distance formula when finding the radius given the center of a circle and a point on the circle.

• Teachers will build procedural fluency from conceptual understanding by showing the relationship between the use of the midpoint formula when finding the center given the endpoints of the diameter of the circle.

## Misconceptions

• Students understand how to use the distance formula to find the length of the radius of a circle given the center and a point on the circle.

• Students understand how to use the midpoint formula to find the center of a circle given the endpoints of the diameter.

• Students don’t make the connection that application of the distance formula can be used to find the length of the radius when given the center and a point on the circle.

• Students don’t make the connection that the midpoint formula can be used to find the coordinates of the center when given the endpoints of the diameter.

OKMath Framework Introduction