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“Transformations On a four quadrant coordinate grid

“Transformations On a four quadrant coordinate grid. Leigha Mod 2. translation. A translation (slide) is a transformation that moves all points of the figure a given distance in a given direction. A(-2,3) B(-2,1) C(-5,1) A’(4,-1) B’(4,-3) C’(1,-3). Rule:(X,Y)  (X+4,Y+6). dilation.

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“Transformations On a four quadrant coordinate grid

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  1. “TransformationsOn a four quadrant coordinate grid Leigha Mod 2

  2. translation • A translation (slide) is a transformation that moves all points of the figure a given distance in a given direction. A(-2,3) B(-2,1) C(-5,1) A’(4,-1) B’(4,-3) C’(1,-3) Rule:(X,Y) (X+4,Y+6)

  3. dilation • A dilation is a transformation that produces an image similar to the original figure. • The scale factor is the ratio of the original and new dimensions. • If the scale factor of a dilation is greater than 1, the image is an enlargement, which is larger than the original figure. • If the scale factor is between 0 and 1, the image is a reduction, which is smaller than the original figure.

  4. reduction A(-2,-2) B(1,-1) C(0,2) A’(-4,-4) B’(2,-2) C’(0,4) Rule: triangle A’B’C’ is 0.5 the size of ABC

  5. enlargement A(2,1) B(-1,3) C(-3,-2) A’(4,2) B’(-2,6) C’(-6,-4) Scale Factor: Triangle A’B’C’ is twice the size of ABC

  6. Reflection/line symmetry • A reflection is a transformation in which a figure is reflected, or flipped, in a line, called the line of reflection. • A figure has line symmetry if a line, called the line of symmetry, divides the figure into two parts that are reflections of each other in the line.

  7. Reflection over the Y-axis A(2,2) B(4,4) C(5,1) A’(-2,2) B’(-4,4) C’(-5,1) Rule: Over the Y-axis- Multiply the X-coordinate by -1 and use the same Y-coordinate (X,Y)(-X,Y)

  8. Reflection over the X-Axis A(-7,-6) B(-4,-6) C(-4,-2) A’(7,-6) B’(4,-6) C’(4,-2) ‘ A B B’ C’ Rule: Over the X axis- Use the same X-coordinate and multiply the Y-coordinate by -1 (X,Y)(X,-Y)

  9. Rotational symmetry • A rotation is a transformation in which a figure is turned about a fixed point, called the center of rotation. The angle of rotation is formed by rays drawn from the center of rotation through corresponding points on an original figure and its image. • A figure has rotational symmetry if a rotation of 180 degrees or less clockwise (or counterclockwise) about its center produces an image that fits exactly on the original figure.

  10. Counter-clockwise 90 degreesof turn • Switch coordinates and times • The new X-coordinate by -1 • (X,Y)(-Y,X) A-(1,1) B(4,1) C(4,4) A'(-1,1) B'(-1,4) C'(-4,4)

  11. Clockwise 90 degrees of turn • Switch coordinates and times • the new Y-coordinate by -1 • (X,Y)(Y,-X) B A C A(1,1) B(1,3) C(5,1) A'(1,-1) B'(3,-1) C'(1,-5) A B C

  12. CLOCKWISE OR COUNTER-CLOCKWISE 180 DEGREES OF TURN • Multiply each coordinate by -1 • (X,Y)(-X,-Y) • A (-5,5) • B-(-1,5) • C(-5,2) • D(-1,2) • A'(5,-5) • B(1,-5) • C(5,-2) • D(1,-2) A A B B C C D D

  13. ANGLES OF ROTATION/LINES OF SYMMETRY • 360 degrees divided by the # of points • A 9 sided shape has rotational symmetry • Angle measurements: • 40 degrees-turn 1 • 80 degrees-turn 2 • 120 degrees-turn 3 • 160 degrees-turn 4 • 200 degrees-turn 5 • 240 degrees-turn 6 • 280 degrees-turn 7 • 320 degrees-turn 8 • 360 degrees-turn 9 9/360=40

  14. Thhhheendddddddd Byeeee(;

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