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8.7 translations and rotations 2

The document is about transformations, specifically translations and rotations. It provides examples of performing different types of rotations on sets of points, including 90° clockwise rotations, 90° counterclockwise rotations, and 180° rotations. It explains that a 90° clockwise rotation switches the x and y coordinates and changes the sign of y, a 90° counterclockwise rotation switches the x and y coordinates and changes the sign of x, and a 180° rotation changes the sign of both the x and y coordinates. Several examples are worked through to demonstrate how to find the image of a set of points after a given rotation.

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Daily Homework Quiz For use after Lesson 8.7 2. Where have you seen a translation today? 1. RST has vertices R (–1, 4) , S (3, 4) , and T (2, –3) . Find the vertices of its image after the translation ( x , y ) -> ( x – 4 , y + 5). ∆
Daily Homework Quiz For use after Lesson 8.7 2. Where have you seen a translation today? 1. RST has vertices R (–1, 4) , S (3, 4) , and T (2, –3) . Find the vertices of its image after the translation ( x , y ) -> ( x – 4 , y + 5). ∆ ANSWER R' (–5, 9), S' (–1, 9), T' (–2, 2)
Translations and Rotations Section 8.7 P. 439 - 443
Essential Questions What are the similarities and differences among transformations? How are the principles of transformational geometry used in art, architecture and fashion? What are the applications for transformations?
A rotation is a transformation that “TURNS” each point of a figure the same number of degrees around a common point. For our lessons, that point will be the origin (0,0). Rotations may be clockwise or counterclockwise.
A rotation is a transformation that “TURNS” each point of a figure the same number of degrees around a common point. For our lessons, that point will be the origin (0,0). Rotations may be clockwise or counterclockwise.
 
 
 
Rotation : 90 degrees clockwise switch the coordinates around, and Y will become the opposite sign of the original point. (y, -x) 90 degrees counterclockwise switch the coordinates around, and X will become the opposite sign. (-y, x) 180 degrees “ opposite” coordinates for both x and y. (-x, -y)
Try this on graph paper! A 90 degrees clockwise rotation will switch the coordinates around, and Y will become the opposite sign of the original point. Example P (6,2) P’ (2,- 6) Q (-3,4) Q’ ( , ) W(4,0) W’ ( , )
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after a 90° clockwise rotation. Switch the coordinates around, and Y will become the opposite sign of the original point. (y, -x) A’ (1,-1) B’ (1, -3) C’ (3, -3) D’ (4, -1)
GUIDED PRACTICE for Example 2 and 3 Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after the given rotation. A’ (1,-1) B’ (1, -3) C’ (3, -3) D’ (4, -1) RULE: Switch the coordinates around, and Y will become the opposite sign of the original point. (y, -x) 2. 90 clockwise ANSWER
Try these on graph paper 90 degrees counterclockwise rotation will switch the coordinates around, and X will become the opposite sign. Example: P (5, 3) P’ (-3, 5) Q (-4,-2) Q’ (2, -4) W (-7, 8) W’ ( , )
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after a 90° counterclockwise rotation. Switch the coordinates around, and X will become the opposite sign. (-y, x) A’ (-1,1) B’ (-1, 3) C’ (-3, 3) D’ (-4, 1)
GUIDED PRACTICE for Example 2 and 3 Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after the given rotation. A’ (-1,1) B’ (-1, 3) C’ (-3, 3) D’ (-4, 1) RULE: Switch the coordinates around, and X will become the opposite sign. (-y, x) 3. 90 counterclockwise ANSWER
180 degree rotations will create “opposite” coordinates for both x and y. Example: P (4, 1) P’ (-4, -1) Q(-3, 5) Q’ (3, -5) W (2, -7) W’ ( , ) 180 degrees can be either clockwise or counterclockwise, the result is the SAME!
GUIDED PRACTICE for Example 2 and 3 Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after a 180° rotation. “ opposite” coordinates for both x and y. (-x, -y) A’ (-1,-1) B’ (-3, -1) C’ (-3, -3) D’ (-1, -4)
GUIDED PRACTICE for Example 2 and 3 Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after the given rotation. A’ (-1,-1) B’ (-3, -1) C’ (-3, -3) D’ (-1, -4) RULE: “opposite” coordinates for both x and y. (-x, -y) 4. 180 ANSWER
Homework Page 441 #1-3, 9, 11, 12