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High School: Geometry: Expressing Geometric Properties with Equations

HSG.GPE.A.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.

HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

HSG.GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

HSG.GPE.B.4

Use coordinates to prove simple geometric theorems algebraically.

HSG.GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

HSG.GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.