Common Core: Expressing Geometric Properties with Equations

HSG.GPE.A1

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.

October 1, 2018
HSG.GPE.A2

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

October 1, 2018
HSG.GPE.A3

(+) 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.

October 1, 2018
HSG.GPE.B4

Use 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).

October 1, 2018
HSG.GPE.B5

Prove 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).

October 1, 2018
HSG.GPE.B6

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

October 1, 2018
HSG.GPE.B7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

October 1, 2018