Geometry Transformations

Transcription

1 Geometry Transformations NAME Period 1

2 Transformations Notes Transformation: Maps an, called a, onto a final, called an. Reflection: a transformation representing a of a figure Reflecting over the x-axis, the pre- point (x, y) becomes. Reflecting over the y-axis, the pre- point (x, y) becomes. Ex: Reflect the pre- below around the x-axis. pre- M(-5, 8) M (, ) A(4, 3) A (, ) T(8, -3) T (, ) H(-7, -4) H (, ) 2

3 Translation: a transformation that moves all of a figure the same distance in the same When translating a figure: down to the up from the right to the left from the Ex: Translate the pre- given below up 3 units and to the right 2 units. Pre- A(-3, 3) A (, ) B(3, -4) B (, ) C(-5, -2) C (, ) 3

4 Rotation: a transformation that turns every point of a around a given When rotating a figure 90 counterclockwise, the pre- point (x, y) becomes. When rotating a figure 90 clockwise, the pre- point (x, y) becomes. Ex: Rotate the pre- below 90 counterclockwise around the origin. Pre- X(7, 3) X (, ) Y(8, -5) Y (, ) Z(2, -7) Z (, ) 4

5 Dilation: a transformation that changes the of a figure To dilate a figure, take the of each side of the pre- and by the to get the lengths of the. Ex: Dilate the pre- below by a scale factor of ½ units centered at the origin. pre- L(0, 0) L (, ) M(0, -8) M (, ) N(-8, -8) N (, ) O(-8, 0) O (, ) Isometry: a mapping for which the original figure, the, and its are Ex: Symmetry: some figures can be folded so that the two halves match exactly The fold is a line of called a. Ex: Determine the number of lines of symmetry in each figure. 5

6 Transformations - Assignments Reflections Use the coordinate plane below to complete problems one and two. 1.) Draw quadrilateral KLMN with vertices K(-3, -4), L(-6, 3), M(-9, 2), and N(-8, -4). Reflect this quadrilateral over the x-axis. Label the new vertices K L M N. Fill in the coordinates in the chart below. 2.) Draw triangle XYZ with vertices X(2, 3), Y(6, 7), and Z(4, 10). Reflect this triangle over the x-axis. Label the new vertices X Y Z. Fill in the coordinates in the chart below. pre- K(-3, -4) K (, ) L(-6, 3) L (, ) M(-9, 2) M (, ) N(-8, -4) N (, ) X(2, 3) X (, ) Y(6, 7) Y (, ) Z(4, 10) Z (, ) 6

7 Use the coordinate plane below to complete problems three and four. 3.) Draw triangle ABC with vertices A(-7, -2), B(-6, -7), and C(-2, -4). Reflect this triangle over the y-axis. Label the new vertices A B C. Fill in the coordinates in the chart below. 4.) Draw triangle DEF with vertices D(-5, 1), E(-7, 5), and F(-1, 8). Reflect this triangle over the y-axis. Label the new vertices D E F. Fill in the coordinates in the chart below. pre- A(-7, -2) A (, ) B(-6, -7) B (, ) C(-2, -4) C (, ) D(-5, 1) D (, ) E(-7, 5) E (, ) F(-1, 8) F (, ) 7

8 Translations Use the coordinate plane below to complete problems five and six. 5.) Draw triangle JKL with vertices J(-8, -3), K(-3, -1), and L(-5, -6). Move this triangle up 6 units. Label the new vertices J K L. Fill in the coordinates in the chart below. 6.) Draw triangle MNO with vertices M(8, 3), N(9, -1), and O(6, 0). Move this triangle to the left 5 units. Label the new vertices M N O. Fill in the coordinates in the chart below. pre- J(-8, -3) J (, ) K(-3, -1) K (, ) L(-5, -6) L (, ) M(8, 3) M (, ) N(9, -1) N (, ) O(6, 0) O (, ) 8

9 Use the coordinate plane below to complete problems seven and eight. 7.) Draw quadrilateral MATH with vertices M(-9, 8), A(-2, 7), T(-1, 4), and H(-7, 3). Move this quadrilateral to the right 7 units. Label the new vertices M A T H. 8.) Now move M A T H down 9 units. Label the new vertices M A T H. Fill in the coordinates in the chart below. pre- M(-9, 8) M (, ) A(-2, 7) A (, ) T(-1, 4) T (, ) H(-7, 3) H (, ) 9

10 Rotations Use the coordinate plane below to complete the following steps in rotating a figure 90 counterclockwise about the origin (0, 0). 9.) Draw triangle BOG with vertices B(3, 1), O(7, 1), and G(5, 6). Place a point at the origin (0, 0) and label it A. Then draw a segment connecting A to B. Measure AB. Use a protractor to create a 90 counterclockwise angle from this segment. Create a new segment the same length as AB and label it AB '. Repeat the above steps wit the other two vertices (O and G) of triangle BOG. Connect the vertices to form you rotated triangle. Fill in the coordinates in the chart below. (*** Only use measurements and a protractor if need!) pre- B(3, 1) B (, ) O(7, 1) O (, ) G(5, 6) G (, ) 10

11 Use the coordinate plane below to rotate a figure 90 clockwise about the origin. 10.) Draw triangle RDS with vertices R(-8, 4), D(-2, 3), S(-7, -1). Follow the same steps as problem 9 but rotate the figure 90 clockwise. Label the rotated triangle R D S. Fill in the coordinates in the chart below. pre- R(-8, 4) R (, ) D(-2, 3) D (, ) S(-7, -1) S (, ) 11

12 Dilations Use the coordinate plane below to dilate a figure by a scale factor of 2 centered at the origin. 11.) Draw square ABCD with vertices A(0, 0), B(-5, 0), C(-5, -5), and D(0, -5). Take the measurement of each side of square ABCD and double it to create a new triangle 2 times as big as the first one with A at the origin. Label the new triangle A B C D. Fill in the coordinates in the chart below. pre- A(0, 0) A (, ) B(-5, 0) B (, ) C(-5, -5) C (, ) D(0, -5) D (, ) 12

13 Use the coordinate plane below to dilate a figure by a scale factor of ½ centered at the origin. 12.) Draw rectangle NOTE with vertices N(0, 0), O(6, 0), T(6, 4), and E(0, 4). Take ½ of the measurement of each side of rectangle NOTE to create a rectangle that is ½ the size of the original. Label the new rectangle N O T E. Fill in the coordinates in the chart below. pre- N(0, 0) N (, ) O(6, 0) O (, ) T(6, 4) T (, ) E(0, 4) E (, ) 13

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