G-GPE: Geometry - Expressing Geometric Properties with Equations

Geometry - Expressing Geometric Properties with Equations

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Expressing Geometric Properties with Equations connects coordinate geometry to algebraic representations of lines, parabolas, and circles. Key standards include deriving the distance and midpoint formulas and using coordinates to prove geometric theorems. Content appears in Geometry and Precalculus.

G-GPE.ATranslate between the geometric description and the equation for a conic section.G-GPE.BUse coordinates to prove simple geometric theorems algebraically.
Example Problems
The equation of an ellipse is given below.


What is its center?
Find the distance, , between and .
Express your answer in exact terms and simplify, if needed.
Write the equation for a parabola with a focus at and a directrix at .
Point M is the midpoint of point A and point B. Find the coordinates of point B.


The equation of a circle is given below.


What is its center?
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