MA.912.GR.3.2

Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.

Examples

Example: Given Triangle ABC has vertices located at (-2,2), (3,3) and (1,-3), respectively, classify the type of triangle ABC is.

Example: If a square has a diagonal with vertices (-1,1) and (-4,-3), find the coordinate values of the vertices of the other diagonal and show that the two diagonals are perpendicular.

Clarifications

Clarification 1: Instruction includes using the distance or midpoint formulas and knowledge of slope to classify or justify definitions, properties and theorems.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.GR.3.AP.2: Use coordinate geometry to classify definitions, properties and theorems involving circles, triangles, or quadrilaterals.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Midpoints of Sides of a Quadrilateral:

Students are asked to prove that the quadrilateral formed by connecting the midpoints of the sides of a given quadrilateral is a parallelogram.

Type: Formative Assessment

Type of Triangle:

Students are given the coordinates of three vertices of a triangle and are asked to use algebra to determine whether the triangle is scalene, isosceles, or equilateral.

Type: Formative Assessment

Diagonals of a Rectangle:

Students are given the coordinates of three of the four vertices of a rectangle and are asked to determine the coordinates of the fourth vertex and show the diagonals of the rectangle are congruent.

Type: Formative Assessment

Describe the Quadrilateral:

Students are given the coordinates of the vertices of a quadrilateral and are asked to determine whether the quadrilateral could also be a parallelogram, rhombus, rectangle, square, or trapezoid.

Type: Formative Assessment

Triangle Midsegment Proof:

Students are asked to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side of the triangle and half of its length.

Type: Formative Assessment

MFAS Formative Assessments

Describe the Quadrilateral:

Students are given the coordinates of the vertices of a quadrilateral and are asked to determine whether the quadrilateral could also be a parallelogram, rhombus, rectangle, square, or trapezoid.

Diagonals of a Rectangle:

Students are given the coordinates of three of the four vertices of a rectangle and are asked to determine the coordinates of the fourth vertex and show the diagonals of the rectangle are congruent.

Midpoints of Sides of a Quadrilateral:

Students are asked to prove that the quadrilateral formed by connecting the midpoints of the sides of a given quadrilateral is a parallelogram.

Triangle Midsegment Proof:

Students are asked to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side of the triangle and half of its length.

Type of Triangle:

Students are given the coordinates of three vertices of a triangle and are asked to use algebra to determine whether the triangle is scalene, isosceles, or equilateral.

Student Resources

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Parent Resources

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