Rotations Coordinate Algebra 5 3 Rotations are isometries

Rotations Coordinate Algebra 5. 3

Rotations are isometries because they preserve shape and size

Rotations on the Coordinate Plane • You can rotate figures clockwise or counterclockwise on the coordinate plane Counter. Clockwise

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This shows how a triangle can be rotated counterclockwise about the origin

Rules for rotating about the origin (Copy these on your organizer) • • 0 degrees 90 deg CW 90 deg CCW 180 degrees 270 deg CW 270 deg CCW 360 degrees (x, y) (x, y) (y, -x) (-y, x) (-x, -y) (-y, x) (y, -x) (x, y) Remember, when you are rotating a figure, rotate each vertex individually, then redraw your figure!

That was a lot of rules!! So, to recap: • 0, 360 - coordinates stay the same • 180 - change both signs • 90, 270 - reverse the order and use coordinate plane to help determine the signs (I will show you what I mean on the next few slides)

If You Rotate And You Know It! • If it’s 0 or 360, stay the same • To rotate 180 degrees, change the signs • But if it’s 90 or 270, reverse the order and draw a graph, move the point, and use the signs of the quadrant!

Rotating Points About the Origin •

Your turn • (1, -8) (6, 3) (-3, 4) (3, 1) (-3, -2)

Rotating a Figure U (2, 0) V (3, -2) L (-1, -3) U’ (-2, 0) V’ (-3, 2) L’ (1, 3)

Rotating a figure I (-3, 3) N(-2, 3) W(2, 1) D(-1, -1) I’ (3, 3) N’ (3, 2) W’(1, -2) D’(-1, 1)

Writing Rules for the Rotations Rotation 270 degrees clockwise about the origin Rotation 180 degrees clockwise about the origin OR OR Rotation 90 degrees counter clockwise about the origin Rotation 180 degrees counter clockwise about the origin

Rotations Day 2 • Mapping figures onto themselves • Rotating about other points

Describe the rotations that would map the following regular polygons to itself • To do this, take 360 and divide by the number of sides. Then find the multiples of that number • Pentagon – 360/5 – 72, 144, 216, 288, 360 • Octagon – 360/8 – 45, 90, 135, 180, 225, 270, 315, 360 • Triangle – 360/3 – 120, 240, 360

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