Standard 3: Use coordinate geometry to solve problems or prove relationships.

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General Information
Number: MA.912.GR.3
Title: Use coordinate geometry to solve problems or prove relationships.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.GR.3.AP.1
Select the weighted average of two or more points on a line.
MA.912.GR.3.AP.2
Use coordinate geometry to classify definitions, properties and theorems involving circles, triangles, or quadrilaterals.
MA.912.GR.3.AP.3
Use coordinate geometry to solve mathematical geometric problems involving lines, triangles and quadrilaterals.
MA.912.GR.3.AP.4
Solve mathematical and/or real-world problems on the coordinate plane involving perimeter or area of a three- or four-sided polygon.

Related Resources

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

Formative Assessments

Partitioning a Segment:

Students are asked to find the coordinates of a point which partitions a segment in a given ratio.

Type: Formative Assessment

Centroid Coordinates:

Students are asked to find the coordinates of the centroid when given the ratio of a directed segment.

Type: Formative Assessment

Proving Slope Criterion for Perpendicular Lines - 2:

Students are asked to prove that if the slopes of two lines are both opposite and reciprocal, then the lines are perpendicular.

Type: Formative Assessment

Proving Slope Criterion for Perpendicular Lines - 1:

Students are asked to prove that the slopes of two perpendicular lines are both opposite and reciprocal.

Type: Formative Assessment

Proving Slope Criterion for Parallel Lines - Two:

Students are asked to prove that two lines with equal slopes are parallel.

Type: Formative Assessment

Proving Slope Criterion for Parallel Lines - One:

Students are asked to prove that two parallel lines have equal slopes.

Type: Formative Assessment

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

Perimeter and Area of an Obtuse Triangle:

Students are asked to find the perimeter and area of an obtuse triangle given in the coordinate plane.

Type: Formative Assessment

Perimeter and Area of a Right Triangle:

Students are asked to find the perimeter and the area of a right triangle given in the coordinate plane.

Type: Formative Assessment

Perimeter and Area of a Rectangle:

Students are asked to find the perimeter and the area of a rectangle given in the coordinate plane.

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

Pentagon’s Perimeter:

Students are asked to find the perimeter of a pentagon given in the coordinate plane.

Type: Formative Assessment

Lesson Plans

Keeping Triangles in Balance: Discovering Triangle Centroid is Concurrent Medians:

In this lesson, students identify, analyze, and understand the Triangle Centroid Theorem. Students discover that the centroid is the point of concurrency for the medians of a triangle and recognize its associated usage with the center of gravity or barycenter. This set of instructional materials provides the teacher with hands-on activities using technology as well as paper-and-pencil methods.

Type: Lesson Plan

Just Plane Ol' Area!:

Students will construct various figures on coordinate planes and calculate the perimeter and area. Use of the Pythagorean theorem will be required.

Type: Lesson Plan

Original Student Tutorial

High Tech Seesaw:

Learn how to find the point on a directed line segment that partitions it into a given ratio in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiasts

Amping Up Violin Tuning with Math:

Kyle Dunn, a Tallahassee-based luthier and owner of Stringfest, discusses how math is related to music. 

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Cataloging Cats with Cartesian Coordinates:

This researcher knows where your cat lives! Watch how he uses coordinates and the distance formula to plot the location of hundreds of thousands of cats on a map.

Type: Perspectives Video: Professional/Enthusiast

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorial

High Tech Seesaw:

Learn how to find the point on a directed line segment that partitions it into a given ratio in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast