Unit 6: Coordinate Geometry

Students bring algebra and geometry together by working with transformations as functions, equations of circles and parabolas, equations of lines (parallel and perpendicular), coordinate proofs of geometric theorems, and weighted averages.

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Unit

Review the unit’s main ideas.

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Concept

Start with the core idea.

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Practice

Build fluency with more questions.

Set 1

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Set 2

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Advanced

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Set 1

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Set 2

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What this unit covers

A Transformations in the Plane · 3 lessons

Goals

• Compare and contrast rigid transformations, similarity transformations, and those that are neither.
• Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

Lessons

1. Rigid Transformations in a Plane
2. Transformations as Functions
3. Types of Transformations

B Distances, Circles, and Parabolas · 5 lessons

Goals

• Calculate the center and radius of a circle by completing the square.
• Use the Pythagorean Theorem to write an equation for a parabola given its focus and directrix.

Lessons

1. Distances and Circles
2. Squares and Circles
3. Completing the Square
4. Distances and Parabolas
5. Equations and Graphs

C Proving Geometric Theorems Algebraically · 9 lessons

Goals

• Calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.
• Calculate the intersection point of a triangle’s medians.
• Determine equations for lines, through a given point, that are parallel or perpendicular to a given line.

Lessons

1. Equations of Lines
2. Parallel Lines in the Plane
3. Perpendicular Lines in the Plane
4. It’s All on the Line
5. Intersection Points
6. Coordinate Proof
7. Weighted Averages
8. Weighted Averages in a Triangle
9. Lines in Triangles

D Let’s Put It to Work · 1 lesson

Lessons

1. Applying Area and Perimeter on the Plane