Rotations Coordinate Algebra 5.3.

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Presentation transcript:

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 Clockwise

Rotating Clockwise!!!!! 0 ° 360 ° 270 ° 90 ° 180 °

This shows how a triangle can be rotated counter-clockwise about the origin

Rules for rotating about the origin (Copy these on your organizer) 0 degrees (x, y) (x, y) 90 deg CW (x, y) (y, -x) 90 deg CCW (x, y) (-y, x) 180 degrees (x, y) (-x,-y) 270 deg CW (x, y) (-y, x) 270 deg CCW (x, y) (y, -x) 360 degrees (x, y) (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 (2, 4) 90 ° clockwise (-3, 6) 180 ° counter-clockwise (-7, -3) 270 ° clockwise (5, -4) 90 ° counter-clockwise (7, -2) 360 ° counter-clockwise

Your turn (1, -8) (6, 3) (-3, 4) (3, 1) (-3, -2) (-1, 8) 180 ° clockwise (3, -6) 90 ° counter-clockwise (-4, -3) 270 ° counter- clockwise (3, 1) 0 ° (-2, 3) 270 ° clockwise (6, 3) (-3, 4) (3, 1) (-3, -2)

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

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

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

What would be the difference between rotating this figure about the origin versus rotating about the point (1, -3)?