EOCT Review
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Transcript of EOCT Review
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EOCT Review
Unit 5 – Transformations in the PlaneUnit 6 – Connecting Algebra with Geometry
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Key Ideas
Precise definitions: Angle Circle Perpendicular lines Parallel lines Line Segment
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Unit 5 - Transformations
Represent transformations in the plane Compare rigid and non-rigid▪ Translations▪ Rotations▪ Reflections
Understand Dilations
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Key Ideas
Given shapes – Determine which sequence of rotations
and reflections would map it on itself
Develop definitions of rotations, reflections and translations
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Translations
A translation maps every two pointsP and Q to points P' and Q' so thatthe following properties are true:● PP' = QQ'● PP' QQ'
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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.
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RotationsA rotation of x° about a point Q maps everypoint S to S' so that the following propertiesare true:● SQ = S' Q and m<SQS' = x° .● Preimage point Q and image point Q' arethe same.Note: QS and QS' are radii of a circlewith center Q.
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Examples
Use the translation (x, y) → (x – 3, y + 1).
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Examples
Describe every transformation that maps the given figure to itself.
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Unit 6 – Connecting Algebra and Geometry
Use coordinates to prove simple geometric theorems algebraically.
Circle centers Parallelograms Rectangles Squares and Rhombii
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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
ym
x
2 1
2 1
y y
x x
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Distance Formula
2 22 1 2 1( ) ( )d x x y y
2 2 2
PythagoreanTheorem
a b c
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Key Ideas
Partition a directed segment into a given ratio. Point P(xp , yp) is found by:
1
1
( )
( )
p
p
ax x run
a ba
y y risea b