#### Unit 4 - Connecting Algebra and Geometry through Coordinates

Contains the following Standard Clusters

• Use coordinates to prove simple geometric theorems algebraically.
• Translate between the geometric description and the equation for a conic section.

## Collection Contents

### Cluster - Use coordinates to prove simple geometric theorems algebraically.

by Allen Wolmer

This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the Unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions. G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem.
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### Cluster - Translate between the geometric description and the equation for a conic section.

by Allen Wolmer

The directrix should be parallel to a coordinate axis.
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