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Unit ActivityUnit: TransformationsThis activity will help you meet these educational goals:Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, construct viable arguments and analyze the reasoning of others, use appropriate tools strategically, attend to precision, look for and make use of structure, and look for and express regularity in repeated reasoning.IntroductionIn this activity, you will apply transformations to two-dimensional shapes and determine the relationship between the transformed shapes and the original shapes.__________________________________________________________________________Directions and AnalysisTask 1: Congruent ShapesPreston says the sequence of transformations that maps triangle ABC onto triangle DEF is: rotate it 180 degrees about the origin, and then translate it up 7 units.Chanel says the sequence of transformations that maps triangle ABC onto triangle DEF is: reflect it across the x-axis, then reflect it across the y-axis, and then translate it up 6 units and left 1 unit.First, take a look at Preston’s sequence. How does a 180-degree rotation about the origin change the coordinates of a shape?Type your response here:Complete the table to find the rule for the rotation, the coordinates of triangle ABC, and the coordinates of the rotated image, triangle A′B′C′.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )A( , )A′( , )B( , )B′( , )C( , )C′( , )How does a translation 7 units up change the coordinates of a shape?Type your response here:Complete the table to find the rule for the translation, the coordinates of triangle A′B′C′, and the coordinates of the translated image, triangle A″B″C″.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )A′( , )A″( , )B′( , )B″( , )C′( , )C″( , )Now look at Chanel’s sequence. How does a reflection across the x-axis change the coordinates of a shape?Type your response here:Complete the table to find the rule for the reflection, the coordinates of triangle ABC, and the coordinates of the reflected image, triangle A′B′C′.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )A( , )A′( , )B( , )B′( , )C( , )C′( , )How does a reflection across the y-axis change the coordinates of a shape?Type your response here:Complete the table to find the rule for the reflection, the coordinates of triangle A′B′C′, and the coordinates of the reflected image, triangle A″B″C″.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )A′( , )A″( , )B′( , )B″( , )C′( , )C″( , )How does a translations 6 units up and 1 unit left change the coordinates of a shape?Type your response here:Complete the table to find the rule for the translation, the coordinates of triangle A″B″C″, and the coordinates of the translated image, triangle A?B?C?.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )A″( , )A?( , )B″( , )B?( , )C″( , )C?( , )Whose sequence proves triangle ABC is congruent to triangle DEF? Why?Type your response here:Task 2: Similar ShapesChanel says the sequence of transformations that maps trapezoid PQRS onto trapezoid KLMN is: rotate it 90 degrees counterclockwise, and then dilate it by a scale factor of .Preston says the sequence of transformations that maps trapezoid PQRS onto trapezoid KLMN is: reflect it across the x-axis, and then dilate it by a scale factor of .Start with Chanel’s sequence. How does a 90-degree counterclockwise rotation about the origin change the coordinates of a shape?Type your response here:Complete the table to find the rule for the rotation, the coordinates of trapezoid PQRS, and the coordinates of the rotated image, trapezoid P′Q′R′S′.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )P( , )P′( , )Q( , )Q′( , )R( , )R′( , )S( , )S′( , )How does a dilation by a scale factor of change the coordinates of a shape?Type your response here:Complete the table to find the rule for the dilation, the coordinates of trapezoid P′Q′R′S′, and the coordinates of the dilated image, trapezoid P″Q″R″S″.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )P′( , )P″( , )Q′( , )Q″( , )R′( , )R″( , )S′( , )S″( , )Now look at Preston’s sequence. How does a reflection across the x-axis change the coordinates of a shape?Type your response here:Complete the table to find the rule for the reflection, the coordinates of trapezoid PQRS, and the coordinates of the reflected image, trapezoid P′Q′R′S′.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )P( , )P′( , )Q( , )Q′( , )R( , )R′( , )S( , )S′( , )How does a dilation by a scale factor of change the coordinates of a shape?Type your response here:Complete the table to find the rule for the dilation, the coordinates of trapezoid P′Q′R′S′, and the coordinates of the dilated image, trapezoid P″Q″R″S″.Type your response here:Original CoordinatesNew Coordinates(x, y)( , )P′( , )P″( , )Q′( , )Q″( , )R′( , )R″( , )S′( , )S″( , )Whose sequence proves trapezoid PQRS is similar to trapezoid KLMN? Why?Type your response here:EvaluationYour teacher will use this rubric to evaluate the completeness of your work as well as the clarity of thinking you exhibit.Total Points: 10Task 1: Congruent ShapesTask points: 5Describe the coordinate change.Find the coordinates after a 180° rotation.Describe the coordinate change.Find the coordinates after a translation up 7.Describe the coordinate change.Find the coordinates after an x-axis reflection.Describe the coordinate change.Find the coordinates after a y-axis reflection.Describe the coordinate change.Find the coordinates after a translation up 6 and left 1.Name the sequence that proves congruence.0.20.60.20.60.20.60.20.60.20.61Task 2: Similar ShapesTask points: 5Describe the coordinate change.Find the coordinates after a 90° counterclockwise rotation.Describe the coordinate change.Find the coordinates after dilation.Describe the coordinate change.Find the coordinates after an x-axis reflection.Describe the coordinate change.Find the coordinates after dilation.Name the sequence that proves similarity.0.250.750.250.750.250.750.250.751 ................
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