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Standards/Math/Mississippi/G-GPE

G-GPE

Mississippi
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Geometry: Expressing Geometric Properties with Equations (G-GPE)
G-GPE.1G-GPE.2G-GPE.3G-GPE.4G-GPE.5G-GPE.6G-GPE.7
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Geometry: Expressing Geometric Properties with Equations (G-GPE)

G-GPE.1Derive 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.G-GPE.2Derive the equation of a parabola given a focus and directrix.G-GPE.3Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.G-GPE.4Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).G-GPE.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).G-GPE.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.G-GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
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