Coordinate Geometry

8 Components
Initial Task
Squares and Rectangles
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Finding Equations of Parallel and Perpendicular Lines
Re-engagement
Re-engagement for Unit 6
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources for GEO Unit 6 Find aligned Regents questions with Quiz Banker
Geo U6: Coordinate Geometry
Browse Components
Initial Task
Squares and Rectangles
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Finding Equations of Parallel and Perpendicular Lines
Re-engagement
Re-engagement for Unit 6
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources for GEO Unit 6 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 1

Line segment relationships are determined by length and direction on the coordinate plane.

1 week
See Standards
Common Core: Major Standards:
G-CO.B.6

Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-SRT.A.1

Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.A.2

Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-GPE.B.5

Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

G-GPE.B.6

Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Evidence of Understanding

  • analyze distance in the coordinate plane and use distance to relate points and lines
    • calculate the distance between two points using the Pythagorean Theorem
    • generalize methods for determining the distance between two coordinate points
      • derive the distance formula using a right triangle and the Pythagorean Theorem
    • explain how the distance formula and Pythagorean Theorem can both be used to find length measurements of segments (or sides of a geometric figure)
    • partition a segment using any point on the segment and find the ratio of its parts
      • describe connections between the partition ratio, dilation, and scale factor
      • given a specified ratio, find the coordinates of a point that partitions a line segment
    • find the coordinates of a segment’s midpoint
      • prove the midpoint of a segment creates two congruent lengths
      • recognize that partitioning a segment with its midpoint bisects the segment in a 1:1 ratio
  • describe direction in the coordinate plane and use direction to relate points and lines
    • given two points, determine the direction of the line containing the two points
    • generalize methods for determining the direction between two coordinate points
      • generate and describe the slope formula using a right triangle
    • dilate a line segment or line and analyze connections between the pre-image and its image
      • make conjectures and use tools to prove parallel lines have the same slope
      • describe connections between parallel lines, dilation, and scale factor
    • rotate a line and analyze the relationship between the slope of the original line and its image
      • show if slopes of two lines have a product of negative one, then they are perpendicular
    • identify and justify if two lines are parallel or perpendicular
    • create equations that represent parallel lines or perpendicular lines
      • given the equation of a line and a specified transformation, determine the equation of its image or pre-image on the coordinate plane

Develop conceptual understanding:

distance formula, partition, midpoint, direction, slope formula, parallel, perpendicular

Supporting terms to communicate:

Pythagorean Theorem, ratio, bisect, dilation, scale factor, similarity, proportion, reciprocal, congruent, rotation

Core Resource

A core resource supports multiple days of instruction.

  • Seeing Segments
    This single-day resource supports students in making connections between the Pythagorean theorem and the Distance formula.
    Resource:
    Seeing Segments

    Geometry & Algebra II Archive

    Geo U6: Coordinate Geometry

    Big Idea: Big Idea 1

    This single-day resource supports students in making connections between the Pythagorean theorem and the Distance formula.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Coordinate Geometry
    File
    Google Doc
    Tags
    activity, distance, pythagorean theorem
    Standards
    Common Core: Major Standards ( G-CO.B.6, G-SRT.A.1, G-SRT.A.2, G-GPE.B.5, G-GPE…
    +— Details
    Common Core: Major Standards:
    G-CO.B.6

    Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

    G-SRT.A.1

    Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

    G-SRT.A.2

    Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

    G-GPE.B.5

    Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

    G-GPE.B.6

    Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

    All Resources From:
Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.