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).

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use coordinates to prove simple geometric theorems algebraically. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes


Geometry - Fluency Recommendations

Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.


  • Item Type(s): This benchmark may be assessed using: ETC item(s)

  • Assessment Limits :
    Items may require the student to use slope or to find the distance
    between points.

    Items may require the student to prove properties of triangles,
    properties of quadrilaterals, properties of circles, and properties of
    regular polygons.

    Items may require the student to use coordinate geometry to provide
    steps to a proof of a geometric theorem.

  • Calculator :


  • Clarification :
    Students will use coordinate geometry to prove simple geometric
    theorems algebraically
  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context.
  • Response Attributes :
    Items may require the student to determine if the algebraic proof is


  • Test Item #: Sample Item 1
  • Question:

    One diagonal of square EFGH is shown on the coordinate grid.

    There are two highlights in the sentence to show which word or phrase may be incorrect. For each highlight, click the word of phrase that is correct.

  • Difficulty: N/A
  • Type: ETC: Editing Task Choice