Notes: Rotations on the coordinate plane Rules for rotations: The following rules can be used to rotate a point 90°, 180°, or 270° counterclockwise about the origin in the coordinate plane. Angle of Procedure in English Visual Procedure in Math rotation 90° Multiply the y-coordinate by -1, then interchange the x- and y-coordinates. 180° Multiply the x- and ycoordinates by -1. 270° Multiply the x-coordinate by -1 then interchange the x- and y-coordinates What about clockwise rotations? 90° clockwise (π₯, π¦) β (βπ¦, π₯) (π₯, π¦) β (βπ₯, βπ¦) (π₯, π¦) β (π¦, βπ₯) 180° clockwise 270° clockwise Graph each figure and its image after the specified rotation about the origin. Example 1) trapezoid FGHI has vertices F(7, 7), G(9, 2), Example 2) β³LMN has vertices L(β1, β1), M(0, β4), and H(3, 2), and I(5, 7); 90° counterclockwise N(β6, β2); 90° clockwise Example 3) β³ABC has vertices A(β3, 5), B(0, 2), and C(β 5, 1); 180° Example 4) parallelogram PQRS has vertices P(4, 7), Q(6, 6), R(3, β2), and S(1, β1); 270° clockwise Name________________________________________________________Period_____________Date_______________ Rotations on the Coordinate Plane Practice Graph each figure and its image after the specified rotation about the origin. 1) β³STU has vertices S(2, β1), T(5, 1) and U(3, 3); 90° 2) β³DEF has vertices D(β4, 3), E(1, 2), and F(β3, β3); clockwise 180° 3) quadrilateral WXYZ has vertices W(β1, 8), X(0, 4), Y(β2, 1) and Z(β4, 3); 270° counterclockwise 4) trapezoid ABCD has vertices A(9, 0), B(6, β7), C(3, β7) and D(0, 0); 270° clockwise TESSELLATIONS A tessellation is when a single shape is a) repeated to tile a plane with no gaps or overlaps. Below is an example of triangle β³RST rotated around the point R. This forms a tessellation. b)

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