Rotations on the Coordinate Plane Rotations on the

Rotations on the Coordinate Plane

Rotations on the Coordinate Plane • Rotations move an object about a central point • Windmill vanes rotate around a central arm as do the hands of a clock

Rotations on the Coordinate Plane • On the coordinate plane, the central point of rotation is the origin

Rotations Mini-Lab • The graph models vanes of a Dutch windmill • What are the measurements of angle COG, angle GOK, angle KOP, and angle POC? F They each measure 90 degrees C G B H E D I A L Q M J K P N

Rotations Mini-Lab • Record the coordinates of each lettered point below: F E (0, 2) G F (-4, 6) A (2, 0) C B G (-5, 5) C (5, 5) H (-1, 1) H E D I I (-2, 0) L (-1, -1) D (1, 1) A M (0, -2) L Q M J (-6, -4) K (-5, -5) B (6, 4) N (4, -6) P (5, -5) J K P N Q (1, -1)

Rotations Mini-Lab • As the windmill turns, each point of one vane will occupy the previous location of the corresponding point on another vane. F C G B H E D I A L Q M J K P N

Rotations Mini-Lab • Compare the coordinates of the vertices of vane ABCD with those of vane EFGH • What do you notice? F A (2, 0) E (0, 2) B (6, 4) F (-4, 6) C (5, 5) G (-5, 5) D (1, 1) H (-1, 1) C G B H E D I A L Q M J K P N They are switched and then the xcoordinate of each point is multiplied by -1.

Rotations Mini-Lab • How many degrees did the vane rotate to move from point C to point G? 90 degrees F C G B H E D I A L Q M J K P N

Rotations Mini-Lab • Compare the coordinates of the vertices of vane ABCD with those of vane IJKL • What do you notice? Both coordinates of F C G A (2, 0) I (-2, 0) B (6, 4) J (-6, -4) C (5, 5) K (-5, -5) D (1, 1) L (-1, -1) each point are multiplied by -1 B H E D I A L Q M J K P N

Rotations Mini-Lab • How many degrees did the vane rotate to move from point C to point K? 180 degrees F C G B H E D I A L Q M J K P N

Rotations Mini-Lab What did we learn? • To rotate a figure 90 degrees counterclockwise, switch the coordinates of each point and then multiply the first coordinate by -1 • To rotate a figure 180 degrees, multiply both coordinates of each point by -1

Rotations Checkpoint • Triangle ABC has vertices A (1, 3), B (6, 7), and C (9, 1). • Rotate the triangle ABC 90 degrees counterclockwise and give the vertices of triangle A’B’C’ A’ (-3, 1) B’ (-7, 6) C’ (-1, 9)

Rotations Checkpoint • Triangle ABC has vertices A (1, 3), B (6, 7), and C (9, 1). • Rotate the triangle ABC 180 degrees and give the vertices of triangle A’B’C’ A’ (-1, -3) B’ (-6, -7) C’ (-9, -1)

Homework • Practice Worksheet 11 -10 • Practice Skills 6 -9 • DUE TOMORROW!!