Transformation. Translation To vertically and/or horizontally a figure. Each point. Reflection. Rotation. Geometry Unit 2: Transformations
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1 Name: Period: Geometry Unit 2: Transformations Mrs. Fahey Main Idea Notes An operation that maps an original figure, called the onto a new figure called the. v Starting point: Transformation v 1 st change: v 2 nd change: v 3 rd change: A transformation can change the,, or of a figure. Can have transformation or a of many. Translation To vertically and/or horizontally a figure. Each point moves the same and. Rule Form: represents the shift represents the shift Reflection A over a line called the. Each point and its image are the distance from line of reflection Possible Lines of Reflection: v - or - v Vertical or Horizontal lines in the form or v Diagonal Lines in the form or Rotation A around a fixed point called the center of rotation. The figure rotates at a specific and. Rules for rotating COUNTERCLOCKWISE about the ORIGIN
2 Translations Experiment! Name: Experiment 1: Step 1: Graph rectangle ABCD anywhere on the graph. Step 2: Record your points under original points on the chart. Step 3: Move the whole rectangle four spaces to the right. Step 4: Record the new points under new points on the chart. New What do you notice about what happened to each of the points? Explain your reasoning below. Experiment 2: Step 1: Graph triangle JKL anywhere on the graph. Step 2: Record your points under original points on the chart. Step 3: Move the whole triangle three spaces up. Step 4: Record the new points under new points on the chart. New What do you notice about what happened to each of the points this time? Explain your reasoning below. In Summary: Suppose a triangle is moved a units to the right and b units up. What would happen to each of the x and y coordinates? Write a rule below: (x, y) (, )
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4 Reflections Experiment! Name: Experiment 1: Step 1: Graph ΔABC anywhere on the graph. Step 2: Record your points under original points on the chart. Step 3: Reflect the whole triangle across the y-axis. Step 4: Record the new points under y-axis on the chart. Step 5: Reflect your original triangle across the x-axis. Step 6: Record these new points under x-axis on the chart. y-axis x-axis What do you notice about what happened to each of the points after reflecting across the y-axis? What do you notice about what happened to each of the points after reflecting across the x-axis? Experiment 2: Step 1: Graph ΔJKL anywhere on the graph. Step 2: Record your points under original points on the chart. Step 3: Reflect ΔJKL across the line already drawn on the graph, y=x. Step 4: Record the new points under y=x on the chart. y = x What do you notice about what happened to each of the points this time? Explain your reasoning below. In Summary: Write rules for each of your experiments below: Reflect across y-axis: (x, y) (, ) Reflect across x-axis: (x, y) (, ) Reflect across y = x: (x, y) (, )
5 Rotations Experiment! Name: Experiment 1: Step 1: Graph ΔABC with points A(1,2), B( 3,4), C( 2, 5). Step 2: Rotate ΔABC 90 counterclockwise. Step 3: Record the new points under 90 on the chart. Step 4: Rotate the original ΔABC 180 counterclockwise. Step 5: Record the new points under 180 on the chart. Step 6: Rotate the original ΔABC 270 counterclockwise. Step 7: Record the new points under 270 on the chart A(1,2) B( 3,4) C( 2, 5) What do you notice about what happened to each of the points after rotating 90? What do you notice about what happened to each of the points after rotating 180? What do you notice about what happened to each of the points after rotating 270? In Summary: Write rules for each of your experiments: Rotate 90 : (x, y) (, ) Rotate 180 : (x, y) (, ) Rotate 270 : (x, y) (, )
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