Standards Map

Mathematics > Course Model Mathematics II (Integrated Pathway) > Expressing Geometric Properties with Equations
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Expressing Geometric Properties with Equations

Cluster - Use coordinates to prove simple geometric thereoms algebraically.

[MII.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).

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.EE.B.6
    Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
  • 8.G.A.3
    Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • 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:

  • MII.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.
  • MII.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.
  • MIII.G-MG.A.1
    Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*