EOCT Review Unit 5 – Transformations in the Plane

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Presentation transcript:

EOCT Review Unit 5 – Transformations in the Plane Unit 6 – Connecting Algebra with Geometry

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 Translations Rotations Reflections Understand Dilations

Key Ideas Given shapes – Determine which sequence of rotations and reflections would map it on itself Develop definitions of rotations, reflections and 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 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 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 Use the translation (x, y) → (x – 3, y + 1).

Examples Describe every transformation that maps the given figure to itself.

Unit 6 – Connecting Algebra and Geometry Use coordinates to prove simple geometric theorems algebraically. Circle centers Parallelograms Rectangles Squares and Rhombii

Geometric Problems y=mx+b 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

Exterior Angle Theorem m<1= m<2+m<3

Key Ideas Partition a directed segment into a given ratio.

Review Examples See Study Guide Handout