Standards Map

Mathematics > Course Model Geometry (Traditional Pathway) > Expressing Geometric Properties with Equations
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Mathematics | Course : Model Geometry (Traditional Pathway)

Domain - Expressing Geometric Properties with Equations

Cluster - Translate between the geometric description and the equation for a conic section.

[GEO.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.

Resources:


  • Pythagorean Theorem
    For any right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.

Predecessor Standards:

  • 8.G.B.8
    Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.A-REI.B.4.a
    Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
  • AI.A-REI.C.7
    Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
  • AI.A-REI.D.10
    Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation.
  • GEO.G-GPE.A.2
    Derive the equation of a parabola given a focus and directrix.
  • GEO.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).