HS.G-GPE: HS.G-GPE

HS.G-GPE

HS.G-GPE.1Derive the equation of a circle of given center and radius. Derive the equation of a parabola given a focus and directrix. (+) Derive the equations of ellipses and hyperbolas given foci, using the fact that the sum or difference of distances from the foci is constant.HS.G-GPE.2Convert between the standard and general form equations of conic sections.HS.G-GPE.3Identify key features of conic sections given their equations. Apply properties of conic sections in real world situations.HS.G-GPE.4Use coordinates to verify simple geometric theorems algebraically. Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral.HS.G-GPE.5Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.HS.G-GPE.6Use coordinates to find the midpoint or endpoint of a line segment. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.HS.G-GPE.7Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids and kites.
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