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MAFS.912.G-GPE.1.1

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Congruence, Similarity, Right Triangles & Trig - 46%

MAFS.912.G-


Circles, Geometric Measurement & Geometric Properties with Equations - 38%

MAFS.912.G-


Modeling with Geometry - 16%

MAFS.912.G-


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What You Need To Know...

MAFS.912.G-GPE.1.1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

1. The benchmark will be assessed using Equation Response, Graphic Response, Hot Text Response, Movable Text Response, Multiple Choice Response or Mult-select Response.

2. Items may require student to find the center and radius of a circle given its equation in general form.

3. Items may require students to create a circle representing an equation in general form.

4. Items may require students to use the Pythagorean theorem using the coordinates of a circle's center and the circle's radius to derive the equation of a circle.

 

Example One

Example Two

Circle Q has a radius of 5 units with center Q(3.7, -2).  Which of the following equations defines circle Q?

  1. (x + 3.7)2 + (y - 2)2 = 5
  2. (x + 3.7)2 + (y - 2)2 = 25 
  3. (x - 3.7)2 + (+ 2)2 = 5 
  4. (x - 3.7)2 + (+ 2)2 = 25  

CLICK HERE FOR SOLUTION

Example Three

Additional Examples

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Distance Formula
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Points on a Circle
Standard Form
Complete the Square
Solve by Completing the Square
Find the Center & Radius

Reference Sheet



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Select sample problems taken from FLDVIPN teacher materials

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Lisa Lasseter - St. Johns Co.
Jeremy Lowery - Escambia Co.
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