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Rotations

TEXTBOOK REFERENCE: 10-9b. Rotations. What are Ro t a t ions?. A ro t a t ion is a figure t urned about the origin (0,0) 2 types: clockwise or counterclockwise Determined by degrees: 90°: ¼ turn and moves one quadrant 180°: ½ turn and moves two quadrants

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Rotations

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  1. TEXTBOOK REFERENCE: 10-9b Rotations

  2. What are Rotations? A rotation is a figure turned about the origin (0,0) 2 types: clockwise or counterclockwise Determined by degrees: 90°: ¼ turn and moves one quadrant 180°: ½ turn and moves two quadrants 270°: ¾ turn (same as 90°in opposite direction) and moves three quadrants.

  3. Counterclockwise Quadrant II Quadrant I Quadrant III Quadrant IV Counterclockwise follows the numbering of the quadrants.

  4. Rotations, cont’d 8 6 4 2 -10 -5 5 10 -2 -4 -6 -8 A (-,+) (+,+) B C (-,-) (+,-) Point A of ABC is (1, 8) Rotating Counterclockwise Point A has the following coordinates. 90°: (-8,1) 180°: (-1,-8) 270°:(8,-1)

  5. Rules for Rotations • Patterns emerge as we look at the ordered pairs. • For 90° and 270°: The x and y change positions and signs. • For 180°: The x and y stay in the same position (but with different signs). • The sign of the ordered pair will always match the quadrant in which it lies.

  6. Formula for Rotations The new rotated coordinates are called prime! • For 90° Counterclockwise: • (x,y) (-y, x) • For 90° Clockwise: • (x,y) (y, -x) • For 180°: • (x,y) (-x,-y) A(9, 1) B(3, -2) C(6, 0) Flip the order, opposite of y A(9, 1) B(3, -2) C(6, 0) Flip the order, opposite of x A(9, 1) B(3, -2) C(6, 0) Opposite of x and y

  7. Rotations Practice Graph triangle ABC with vertices Graph rectangle EFGH E(2, 1) A(-3, 4) B(-1, 1) and C(-3, 1) rotated F(2, 5) G(4, 5) and H(4, 1) rotated 90º counterclockwise about the origin 90º clockwise about the origin

  8. Rotations Practice Graph triangle ABC with vertices Graph rectangle EFGH E(2, 1) A(-3, 4) B(-1, 1) and C(-3, 1) rotated F(2, 5) G(4, 5) and H(4, 1) rotated 180º about the origin 180º about the origin

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