8 Components
Big Ideas
End of Unit Assessments
Browse Components
Big Ideas
End of Unit Assessments
Big Idea:

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

1 week

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

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

All Resources From:
• Unit 6

#### Coordinate Geometry

Instructional Routine: Sharing Skepticism

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

• Transforming a Triangle
Students will use transformations implicitly to confirm that two triangles are congruent in order to find a missing length.
Resource:
Transforming a Triangle

Students will use transformations implicitly to confirm that two triangles are congruent in order to find a missing length. During sharing of strategies and through annotation, the transformations used will be made explicit.

All Resources From:
• Unit 6