Presentation on theme: "Aim: What do we remember about transformations? Do Now: Do Now: Circle what changes in each of the following: Translation: LocationSizeOrientation Dilation:"— Presentation transcript:
Aim: What do we remember about transformations? Do Now: Do Now: Circle what changes in each of the following: Translation: LocationSizeOrientation Dilation: LocationSizeOrientation Reflection: LocationSizeOrientation Rotation: LocationSizeOrientation
Review Translations Regents Question: Pair/Share: Which of the following translations best describes the diagram below? a. 3 units right and 2 units down b. 3 units left and 2 units up c. 3 units left and 2 units up
Review Dilations Some things to remember: When dilating by a scale factor less than one, the figure becomes smaller. Opposite this, when dilating by a scale factor greater than one the figure becomes larger. To calculate a dilation, multiply the x and y values of each point by the scale factor. Regents Question: Graph triangle ABC and its image under D 3. A(2,3), B(2,-1), C(-1,-1)
Review Reflections Pair/Share: Do you remember the three types of reflections?
line reflection point reflection glide reflection
Line Reflections Some things to remember: r y=x (x,y) becomes (y,x) r y=-x (x,y) becomes (-y,-x) r x-axis (x,y) becomes (x,-y) r y-axis (x,y) becomes (-x,y) Regents Question: Angle ABC has been reflected in the x-axis to create angle A'B'C'. Prove that angle measure is preserved under a reflection.
It appears that the angles may be right angles. Let's see if this is true using slopes. Since these slopes are negative reciprocals, these segments are perpendicular, meaning m<ABC = 90º. Since these slopes are negative reciprocals, these segments are perpendicular, meaning m<A'B'C' = 90º. Angle measure is preserved.
Point Reflections Some things to remember: R(0,0) (x,y) becomes (-x,-y) Regents Question: Pair/Share: When dealing with a point reflection in the origin, the origin is the midpoint of the line segments connecting each point to its image. True False
Glide Reflections Some things to remember: a combination of a line reflection and a translation parallel to the line Regents Question: Given triangle ABC: A(1,4), B(3,7), C(5,1); Graph and label the following composition:
Triangle A'B'C' is the reflection in the x-axis. Then triangle A''B''C'' is the translation of T(-5,-2). A''(-4,-6), B''(-2,-9), C''(0,-3)
Rotations Some things to remember: R 90 (x,y) becomes (-y,x) R 180 (x,y) becomes (-x,-y) R 270 (x,y) becomes (y,-x) positive rotations are counter-clockwise Regents Question: A(2,3), B(2,-1), C(-1,-1) Graph triangle ABC under the following rotations:
Symmetries Some things to remember: Line symmetry occurs when two halves of a figure mirror each other across a line Point symmetry occurs when the center point is a midpoint to every segment formed by joining a point to its image Rotational symmetry occurs if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same
Regents questions: Pair/Share: If the alphabet were printed in simple block printing, which capital letters would have BOTH vertical and horizontal symmetry? Does the word NOON possess point symmetry?
Isometries An isometry is a transformation of the plane that preserves length. A direct isometry preserves orientation or order. A non-direct or opposite isometry changes the order (such as clockwise changes to counterclockwise).