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ROTATION. . Rotations in a Coordinate Plane. In a coordinate plane, sketch the quadrilateral whose vertices are A (2, -2), B (4, 1), C (5, 1), and D (5, -1). Then, rotate ABCD 90 counterclockwise about the origin and name the coordinates of the new vertices.

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## ROTATION

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**ROTATION**.**Rotations in a Coordinate Plane**In a coordinate plane, sketch the quadrilateral whose vertices are A(2, -2), B(4, 1), C(5, 1), and D(5, -1). Then, rotate ABCD 90 counterclockwise about the origin and name the coordinates of the new vertices. Figure ABCDFigure A’B’C’D’ A(2, -2) A’(2, 2) B(4, 1) B’(-1, 4) C(5, 1) C’(-1, 5) D(5, -1) D’(1, 5) Notice that the x-coordinate of the image is the opposite of the y-coordinate of the preimage. The y-coordinate of the image is the x-coordinate of the preimage. 90 Counterclockwise: (x, y) → (-y, x) 90 Clockwise: (x, y) → (y, -x)**Steps in Rotating a Figure**• Identify the axis of rotation. • Construct a line from each point to the axis of rotation. • Measure the angle. • Construct a line from the measured angle to the axis of rotation. • Measure the distance of each point to the axis of rotation. • Use the same measurement in locating the position of the image in the line made in step 4. • Do these to each point of the figure. • Connect all the points (image).**Rotate at 180 degrees from the point of origin.**180 Counterclockwise: (x, y) → (-x, -y) 180 Clockwise: (x, y) → (-x,-y) • Rotate at 90 degrees from the point of origin. 90 Counterclockwise: (x, y) → (-y, x) 90 Clockwise: (x, y) → (y, -x)**Tessellation**• Learning Target: • I can apply transformations (reflection, translation and rotation) by making a tessellation. • Tessellation • A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps.**Steps in making a tesselations**• Draw a 4 by 4 squares (each square is 2 inches by 2 inches) in a printing paper. • Draw one square on top of the paper. On this square draw the pattern of your tessellation. • Create your tessellation design by drawing the pattern in the rest of the squares using transformations. • Color your tessellation.**Steps in making a tesselations**5. Using your tessellation, identify the following: (Note: To identify location of squares, think of your design as quadrant I of a Cartesian plane.) a. At least 3 pairs of squares showing reflection. b. At least 3 pairs of squares showing translation. c. At least 3 pairs of squares showing rotation. 6. Describe the rule in each transformation. Sample answers for #5 and #6: (1,4) reflected over y-axis (2,4) (1,1) translated up 1 unit to (1,2) (1,3) rotated 90 degrees clockwise to (2,2)

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