Massachusetts flagMassachusetts: Geometry - Expressing Geometric Properties with Equations Math Standards

7 standards · 2 domains

TRANSLATE BETWEEN THE GEOMETRIC DESCRIPTION AND THE EQUATION FOR A CONIC SECTION.

  • G-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.
  • G-GPE.A.2 Derive the equation of a parabola given a focus and directrix.
  • G-GPE.A.3.a (+) Use equations and graphs of conic sections to model real-world problems.

USE COORDINATES TO PROVE SIMPLE GEOMETRIC THEOREMS ALGEBRAICALLY.

  • G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. 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.B.5 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).
  • G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  • G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).

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