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Transformations

Transformations. There are 4 Types of Transformations…. Translation Reflection Rotation Dilation. Translation. A translation occurs when you slide a figure without changing anything other than its position. A translated figure has the same size and shape as the original figure.

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Transformations

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  1. Transformations

  2. There are 4 Types of Transformations… • Translation • Reflection • Rotation • Dilation

  3. Translation • A translation occurs when you slide a figure without changing anything other than its position. • A translated figure has the same size and shape as the original figure. A’B’C’ is translated 6 places to the right from ABC.

  4. Example translating a figure • ABC has the following coordinates A(-6,1), B(-2,7), C(3,5) • Translate the triangle 4 units to the right and 9 units down to form A’B’C’. A(-6,1)~(-6+4,1-9)=A’(-2,-8) B (-2,7)~(-2+4,7-9)=B’(-2,-2) C(3,5)~(3+4,5-9)=C’(7,-4) To find the new figure, add 4 to each x coordinate and subtract 9 to each y coordinate and plot the points.

  5. Try This… • ABCD has the following coordinates • A(2,4) • B(4,4) • C(5,2) • D(2,1) • Translate ABCD 7 units to the left and 3 units down. A(2,4)~(2-7,4-3)=A’(-5,1) B(4,4)~(4-7,4-3)=B’(-3,1) C(5,2)~(5-7,2-3)=C’(-2,-1) D(2,1)~(2-7,1-3)=D’(-5,-2) For x coordinates -7 For y coordinates -3

  6. Reflection • Occurs when you flips a figure over a given line and its mirror image is created. • A reflected figure has the same size and shape as the original figure. The above image is an example of a reflection.

  7. Example reflecting a figure • ABC has the following coordinates • A(-2,1) • B(2,4) • C(4,2) • Reflect ABC over the x-axis. To reflect the figure, the x-coordinates remain the same and the sign of the y-coordinates becomes opposite. A(-2,1)~A’(-2,-1) B(2,4)~B’(2,-4) C(4,2)~C’(4,-2)

  8. Try This • MATH has the following coordinates: • M(-4,4) • A(-2,2) • T(-3,1) • H(-5,1) • Reflect MATH about the y-axis To reflect this figure, the sign of the x coordinates will change, and the y coordinates will remain the same. M(-4,4)~M’(4,4) A~(-2,2)~A’(2,2) T~(-3,1)~T’(3,1) H~(-5,1)~H’(5,1)

  9. Rotation • Occurs when you turn a figure around a given point. • Figures can be rotated clockwise or counterclockwise. • A rotated figure has the same size and shape as the original figure.

  10. Example of rotating a figure. • JKL has the following coordinates • J(-9,-2) • K(-4,2) • L(-2,-2) • Rotate JKL 90 degrees around J. To rotate the figure, find out how far and over K and L are from J. Then rotate the paper 90 degrees and plot the points. K 5 right, 4 up J 7 right, 0 up J(-9,-2)~J’(-9,-2) K(-4,2)~K’(-5,-7) L(-2,-2)~L’(-9,-9)

  11. Try This… • ABCDE has the following coordinates. • A(0,4) • B(7,4) • C(9,2) • D(7,0) • E(0,0) • Rotate ABCDE 180 degrees about point E. Find how far each point is from E: A up 4 right 0 B up 4 right 7 C up 2 right 9 D up 0 right 7 Rotate the paper 180 degrees and use the info we found to plot the new points. A’ (0,-4) B’ (-7,-4) C’ (-9,-2) D’ (-7,0)

  12. Dilation • Occurs when you enlarge or reduce a figure. • Center of Dilation • The point where figures will be dilated from. • You will normally be dilating using the origin as your center of dilation. • How to dilate • Multiply the coordinates of each vertex (point) by a positive scale factor. • If the scale factor is less than 1, the dilation will be a reduction • If the scale factor is greater than 1, the dilation will be an enlargement

  13. Example of dilating a figure • ABCDE has the following coordinates: • A(0,0) • B(3,3) • C(6,3) • D(6,-3) • E(3,-3) • Dilate ABCDE using a scale factor of 1/3. To dilate, multiply x and y for each point by 1/3 and graph the points

  14. Try This… • ABC has the following coordinates: • A(-2,-2) • B(1,-1) • C(0,2) • Dilate ABC using a scale factor of 2 Multiply x and y of each point by 2 and plot the new points. A(-2,-2)~A’(-4,-4) B(1,-1)~B’(2,-2) C(0,2)~C’(0,4)

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