Unit 5 transformations in the plane unit 6 connecting algebra with geometry
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Unit 5 – Transformations in the Plane Unit 6 – Connecting Algebra with Geometry. EOCT Review. Key Ideas. Precise definitions: Angle Circle Perpendicular lines Parallel lines Line Segment. Unit 5 - Transformations. Represent transformations in the plane Compare rigid and non-rigid

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EOCT Review

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Unit 5 transformations in the plane unit 6 connecting algebra with geometry

Unit 5 – Transformations in the Plane

Unit 6 – Connecting Algebra with Geometry

EOCT Review


Key ideas

Key Ideas

  • Precise definitions:

    • Angle

    • Circle

    • Perpendicular lines

    • Parallel lines

    • Line Segment


Unit 5 transformations

Unit 5 - Transformations

  • Represent transformations in the plane

    • Compare rigid and non-rigid

      • Translations

      • Rotations

      • Reflections

    • Understand Dilations


Key ideas1

Key Ideas

  • Given shapes –

    • Determine which sequence of rotations and reflections would map it on itself

    • Develop definitions of rotations, reflections and translations


Translations

Translations

A translation maps every two points

P and Q to points P' and Q' so that

the following properties are true:

● PP' = QQ'

● PP' QQ'


Reflections

Reflections

A reflection across a line m maps every point R to R' so that the following properties are true:

● If R is not on m, then m is the perpendicular bisector of RR' .

● If R is on m, then R and R' are the same point.


Rotations

Rotations

A rotation of x° about a point Q maps every

point S to S' so that the following properties

are true:

● SQ = S' Q and m<SQS' = x° .

● Preimage point Q and image point Q' are

the same.

Note: QS and QS' are radii of a circle

with center Q.


Examples

Examples

Use the translation (x, y) → (x – 3, y + 1).


Examples1

Examples

Describe every transformation that maps the given figure to itself.


Unit 6 connecting algebra and geometry

Unit 6 – Connecting Algebra and Geometry

  • Use coordinates to prove simple geometric theorems algebraically.

    • Circle centers

    • Parallelograms

    • Rectangles

    • Squares and Rhombii


Geometric problems

Geometric Problems

  • Prove lines parallel or perpendicular

  • The slope of the line through points (x1, y1) and (x2 , y2 ) is

    • Find the equation of a line through a given point

      • y=mx+b


Distance formula

Distance Formula


Exterior angle theorem

Exterior Angle Theorem

m<1= m<2+m<3


Key ideas2

Key Ideas

  • Partition a directed segment into a given ratio.


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