American High School Geometry Unit 9: Transformations Project

timer Asked: Feb 26th, 2019
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Question Description

This project is based on transformations. (reflection, rotation, etc.) There are three questions in total, please look at the assignment to see if you understand it. While doing the Unit project, make sure that you clearly show all your work and do your best to explain your answers. I will be graded on how well I show my understanding of the concepts as well as correct answers. Show your work if needed, give detailed explanation and solution. You will also be reviewed on how well you show your understanding of the concepts as well as correct answers. this is a graded assignment aim to get 100 A+ thank you.

9 To solve these problems you will pull together many concepts and skills that you have studied about transformations. Pull It All Together Visualization You can use visualization to find the image of a figure for a transformation. Task 1 Each figure below is part of a capital letter in the English alphabet. To find the whole letter, combine the figure with its image for the appropriate rotation or reflection. What letter corresponds to each figure? What transformation produces each letter? L T E S S E L A T I O N Transformations You can use transformations to describe a change in the position of a point. Task 2 The arcs in the photo at the right appear to be paths of stars rotating about the North Star. To produce this effect, the photographer set a camera on a tripod and left the shutter open for an extended time. If the photographer left the shutter open for a full 24 hours, each arc would be a complete circle. You can model a star’s “rotation” in the coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position of the star at the moment the camera’s shutter opens. Suppose the shutter is left open for 2 h 40 min, with the arc ending at Pr. y 1 P O P(1, 0) North Star North Star x a. What angle of rotation maps P onto Pr? b. What are the x- and y-coordinates of Pr to the nearest thousandth? c. What translation rule maps P onto Pr? Coordinate Geometry You can use coordinate geometry to prove a dilation image is similar to its preimage. Task 3 4 Copy the graph at the right. On the same set of axes, graph the image of MNOP for a dilation with center (0, 0) and scale factor 2. Use coordinate geometry and the definition of similar polygons to prove that MNOP is similar to its image. 2 Chapter 9 Pull It All Together Copyright © 2011 Pearson Education, Inc. P M x O 602 y 2 N
Unit 9 Project Rubric Task 1 Finds all 12 whole letters. 5 points Identifies correctly either reflection or rotation for each answer. 2 points identifies horizontal, vertical, or slanted reflection or degrees of rotation. 3 points Total 10 points Task 2 Finds correct answer in part a. 1 point Shows calculations for answer in part a. 1 point Uses trigonometry to find x and y coordinates of ​ P​ ’. Rounds correctly. 3 points Finds rule for translation in part c. 2 points Total 7 points Task 3 Graphs dilation. 1 point Proves all sides are proportional. 4 points Proves all angles are congruent. 4 points Writes correct similarity statement. 1 point Total 10 points

Tutor Answer

School: University of Virginia

The solutions are ready, please ask if something is unclear!docx and pdf files are the same

Task 1. The letters are T, E, S, S, E, L, L, A, T, I, O, N.
The corresponding transformations are:

Reflection over a vertical axis
Reflection over a horizontal axis
Rotation 180 degrees
Rotation 180 degrees
Reflection over a horizontal axis
Reflection over an axis 45 degrees up
Reflection over an axis 45 degrees up
Reflection over a vertical axis
Reflection over a vertical axis
Reflection over a horizontal axis
Reflection over a horizontal axis
Rotation 180 degrees

Task 2.
a. We know 24 hours correspond to 360 degrees, so 2 h 40 min correspond to
360° ∙
= 15° ∙ = 𝟒𝟎°.
b. 𝑃′ lies on the unit circle, so its coordinates are
𝑥 ′ = cos(40°) ≈ 𝟎. 𝟕𝟔𝟔, 𝑦 ′ = sin(40°) ≈ 𝟎. 𝟔𝟒𝟑.
c. To compute it, subtract the coordinates of 𝑃 from the coordinates of 𝑃′ :
cos(40°) − 1 ≈ −0.234, sin(40°) − 0 ≈ 0.643.
This gives the translation about 𝟎. 𝟐𝟑𝟒 units to the left and about 𝟎. 𝟔𝟒𝟑 units up.

Task 3. The picture:

Dilation with center at the origin and scale factor 2 transforms (𝑥, 𝑦) to (2𝑥, 2𝑦).
Because 𝑂(0, 0), 𝑃(1, 3), 𝑀(3, 2), 𝑁(3, 0), the images are 𝑂′ (0, 0)...

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