MA.912.GR.3.3

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Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.

Examples

Example: The line x+2y=10 is tangent to a circle whose center is located at (2,-1). Find the tangent point and a second tangent point of a line with the same slope as the given line.

Example: Given M(-4,7) and N(12,-1),find the coordinates of point P on begin mathsize 12px style left parenthesis top enclose M N end enclose right parenthesis end style so that P partitionsbegin mathsize 12px style left parenthesis top enclose M N end enclose right parenthesis end style in the ratio 2:3.

Clarifications

Clarification 1: Problems involving lines include the coordinates of a point on a line segment including the midpoint.

Clarification 2: Problems involving circles include determining points on a given circle and finding tangent lines.

Clarification 3: Problems involving triangles include median and centroid.

Clarification 4: Problems involving quadrilaterals include using parallel and perpendicular slope criteria.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning
Standard: Use coordinate geometry to solve problems or prove relationships.
Date Adopted or Revised: 08/20
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.3: Use coordinate geometry to solve mathematical geometric problems involving lines, triangles and quadrilaterals.

Related Resources

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

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

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

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

MFAS Formative Assessments

Centroid Coordinates:

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

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.

Partitioning a Segment:

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

Proving Slope Criterion for Parallel Lines - One:

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

Proving Slope Criterion for Parallel Lines - Two:

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

Proving Slope Criterion for Perpendicular Lines - 1:

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

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 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

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

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 benchmark.

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