Lesson 5 Definition of Rotation and Basic Properties

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Presentation transcript:

Lesson 5 Definition of Rotation and Basic Properties BASIC RIGID MOTION #3 = Rotation when a figure is moved around a fixed point a specific number of degrees rotation symbol: R Think: A skateboarder doing a 180 or a 360 Intuitively --- “turn” Center of Rotation : The fixed point from which a figure is turned or rotated. NEED TO KNOW number of degrees AND direction NAME THE POSITIVE OR NEGATIVE NUMBER OF DEGREES THE FIGURE IS TO BE ROTATED BY AND NAME WHETHER THE ROTATION IS CLOCKWISE or COUNTERCLOCKWISE

A positive degree of rotation moves the figure counterclockwise. (CCW) A negative degree of rotation moves the figure clockwise. (CW) P Clockwise- the direction the hands on the clock move; when rotating a figure clockwise (CW) the number of degrees is negative Counter-clockwise- the opposite direction the hands on the clock move; when rotating a figure counter-clockwise (CCW) the number of degrees is positive.

LESSON 5: DEFINITION of ROTATIONS

LESSON 5: ROTATIONS in the COORDINATE PLANE 1) First, draw rectangle ABCD. A (2,7) B (8,7) C (8,2) D (2,2) 2) Next, rotate* (turn) ABCD 90 counter-clockwise about (around) the origin. 3) Then hold your paper at the origin and rotate your paper 90 counter-clockwise. Look at the NEW coordinates to find A’. Rotate your paper back to normal and plot A’. Repeat with B, C, and D. 4) Draw rectangle A’B’C’D’. 5) Last, label the coordinates of A’B’C’D’. A’ (___,___) B’ (___,___) C ‘(___,___) D’ (___,___)

R

1) First, draw triangle LMN. 2) Use the rules on the previous page to rotate (turn) triangle LMN 90 counter-clockwise about (around) the origin. L’ (___,___) M’ (___,___) N ‘(___,___) 4) Draw triangle L’M’N’. 5) Label the coordinates of triangle L’M’N’

ROTATION SUMMARY A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle. A rotation preserves lengths of segments. (3) A rotation preserves degrees of angles.