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Circle Geometry Mini-Lessons: Identifying Center and Radius from Equations

This mini-lesson series focuses on understanding circles in geometry. Students will learn to identify the center and radius of a circle from its standard equation in center-radius form. By working through example problems, such as identifying the center and radius from the equations of various circles, students will reinforce their understanding of geometric principles. Each lesson provides multiple-choice questions to challenge their knowledge and application of the concepts. Perfect for high school geometry students.

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Circle Geometry Mini-Lessons: Identifying Center and Radius from Equations

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  1. Geometry Mini-Lesson Circle C is defined by the equation: (x + 4.2)2 + (y − 5.1)2 = 36Which of the following identifies the center C (h, k) and radius of circle C? • C (4.2, −5.1), radius of 36 units • C (−4.2, 5.1), radius of 36 units • C (−4.2, 5.1), radius of 6 units • C (4.2, −5.1), radius of 6 units MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  2. Geometry Mini-Lesson Circle E has center E (1.6, −2.4) and a radius of 4 units.Which of the following equations defines circle E? • (x −1.6)2 + (y + 2.4)2 = 2 • (x − 1.6)2 + (y + 2.4)2 = 16 • (x − 1.6)2 + (y + 2.4)2 = 4 • (x + 1.6)2 + (y − 2.4)2 = 16 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  3. Geometry Mini-Lesson Circle A is shown in the graph below. Which of the following equations defines circle A? • (x − 9)2 + (y − 5)2 = 25 • (x + 9)2 + (y + 5)2 = 25 • (x − 9)2 + (y − 5)2 = 5 • (x + 9)2 + (y + 5)2 = 5 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  4. Geometry Mini-Lesson Circle C is shown in the graph below. Which of the following equations defines circle C? • (x − 2.5)2 + (y + 0.5)2 = 20.25 • (x − 2.5)2 + (y + 0.5)2 = 9 • (x + 2.5)2 + (y − 0.5)2 = 20.25 • (x + 2.5)2 + (y − 0.5)2 = 9 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  5. Geometry Mini-Lesson Circle D is defined by the equation (x + 3.6)2 + (y − 2.9)2 = 49Which of the following identifies the center D (h, k) and radius of circle D? • D (−3.6, 2.9), radius of 49 units • D (3.6, −2.9), radius of 7 units • D (3.6, −2.9), radius of 49 units • D (−3.6, 2.9), radius of 7 units MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  6. Geometry Mini-Lesson Circle F has center F (5.4, −3.9) and a radius of 9 units. Which of the following equations defines circle F? • (x − 5.4)2 + (y + 3.9)2 = 81 • (x − 5.4)2 + (y + 3.9)2 = 3 • (x − 5.4)2 + (y + 3.9)2 = 9 • (x + 5.4)2 + (y − 3.9)2 = 81 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  7. Geometry Mini-Lesson Circle B is shown in the graph below. Which of the following equations defines circle B? • (x − 5)2 + (y − 8)2 = 4 • (x − 5)2 + (y − 8)2 = 16 • (x + 5)2 + (y + 8)2 = 16 • (x + 5)2 + (y − 8)2 = 4 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  8. Geometry Mini-Lesson Circle D is shown in the graph below. Which of the following equations defines circle D? • (x + 1.5)2 + (y − 0.5)2 = 7 • (x + 1.5)2 + (y − 0.5)2 = 12.25 • (x − 1.5)2 + (y + 0.5)2 = 7 • (x − 1.5)2 + (y + 0.5)2 = 12.25 MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

  9. Geometry Mini-Lesson MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

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