Reflecting a Triangle Across the y-Axis: Rigid Transformation Coordinates and Distance Check

Step 1: My Project Plan Theme My theme is nature. I will make a garden using geometric flowers. Inspiration I am inspired by the shapes and patterns in flowers. My design will show growth and creativity. Design Idea I will use a triangle to make a flower petal. I will repeat the petal around a center point to make a flower. Then I will repeat the flower to make a garden. My colors will be purple, blue, and pink. Transformation Plan I will use all three transformations in my design: I will reflect, or flip, my triangle across the 𝑦 y-axis to make a matching petal. I will rotate, or turn, both petals around 𝑃 ( 0 , 0 ) P=(0,0). I will turn them 90 ∘ 90 ∘ , 180 ∘ 180 ∘ , and 270 ∘ 270 ∘ counterclockwise to make a full flower. I will translate, or slide, the whole flower 10 units to the right to make another flower. I will use the Desmos tools to keep each triangle the same size and shape. My Original Polygon My starting shape will be triangle 𝐴 𝐵 𝐶 ABC. Its corners will be 𝐴 ( 1 , 1 ) A=(1,1), 𝐵 ( 2 , 4 ) B=(2,4), and 𝐶 ( 3 , 2 ) C=(3,2). I will plot the points, connect them, and label them. This triangle will be my first flower petal. This kinda looks like a butterfly so lets just say the theme is nature and I'm making a butterfly. {FIX Picture} Milestone Day 2: Digital Transformation Design Project - Desmos Geometry Tool Setup to Create Geometric Art - Focus on Rigid Transformation (Only Reflection) - Student Task List STEP 1: Go to desmos.com/geometry CLICK HERE for the Desmos Geometry Tool Technical Guide. STEP 2: Use the Polygon tool to build your original polygon from your Day 1 sketch, and label its vertices (A, B, C…) with the Text tool. This should be based on your draft from Milestone # 1. STEP 3: Choose a color you can tell apart from its transformed images later. STEP 4: Use the Transform menu to build your reflection AND Identify your line of reflection and label the image (A′, B′, C′). NOTE ABOUT YOUR LINE OF REFLECTION: If needed you can create a line using the line tool that will serve as a the line of reflection. You can also use any segment as your line of reflection. Teacher Notes: Make your own Google Slide or Google Doc to showcase the requested items. See the Virtual Pro-Tip: Screenshots for Your Submission linked here for the specifications of your submission. Share the annotation slide or doc in the milestone day 2 Canvas LMS tread. RECOMMENDATION: Write down the steps you took to make the reflected part of your design AND/OR Save your image so you can recall how you created the image for the final submission. Think ahead: Does every point of my reflected image sit the same distance from the line of reflection as its matching original point, on the opposite side? (Make your answer simple enough to understand while meeting the requirements)PROJECT: The Digital Transformation Design Challenge Your Mission: Create Art Through Geometry ​ Repeating patterns like this are built from figures that are flipped, slid over, and turned. Artists, architects, designers, and engineers use geometric patterns to create designs that communicate ideas, represent identities, and make spaces visually interesting. Think of a stained-glass window in a school entryway: every colored panel is a shape, and every repeated shape is the result of a figure being flipped, slid, or turned. For this project, you will become a Geometric Designer. Using the Desmos Geometry construction tool, you will create an original digital design that communicates an idea, represents something meaningful to you, or reflects a theme you care about. Your design must demonstrate your understanding of the three rigid transformations you have studied. Your goal is not simply to create an attractive design. You must show that you can use rigid transformations accurately and explain the mathematics behind your work. Because this is a virtual course, everything you create will be built and submitted digitally: your design, your labeled screenshots, and your written statement all go through the assignment in your online course. ​ Key Terms Rigid transformation — a move that repositions a figure without changing its size or shape. Reflection — flipping a figure across a line. Translation — sliding a figure in a particular direction and distance. Rotation — turning a figure around a center through a specified angle and direction. Part 1: Create and Label Your Original Polygon Your original figure is the starting point for every transformation in your design, so build it first and label it carefully. Click the Polygon tool in the toolbar. Click on the workspace to place each vertex of your polygon. Click at least three points to make a triangle, or four or more for a quadrilateral or other polygon. Click back on your first point (or double-click the last point) to close the polygon. Desmos connects the vertices and fills the shape. To label the vertices, select the Text tool, then click near each vertex and type its name, such as A, B, C. To change the color of your polygon, click and hold (or right-click) the shape, choose Edit, and pick a color. Choose a color you can tell apart from its transformed images later. ​ Why labels matter: Your final submission must clearly identify each original figure and its image. Labeling the vertices of your original polygon now — before you transform it — makes every later annotation easier to write and easier for a reader to follow. Part 2: Use the Reflection Tool A reflection flips your figure across a line, like the figure's image in a mirror. The line you reflect across is called the line of reflection. Select the polygon you want to reflect by clicking it. Open the Transform menu in the toolbar and choose Reflect. Desmos now asks you to select the line of reflection. Click an existing line in your workspace, or click two points to define a new line of reflection. The reflected image appears instantly on the other side of the line. Check your result: every point of the image should sit the same distance from the line of reflection as the matching point of the original, on the opposite side. Label the reflected image (for example, A′, B′, C′ — read "A prime") so a viewer can tell the original and the image apart. Part 3: Use the Translation Tool A translation slides your figure in a straight line without turning it. You describe the slide by a vector — an arrow that shows the direction and the distance of the move. Select the polygon you want to translate. Open the Transform menu and choose Translate. Desmos asks you to define the vector. Click a point on your figure, then click where that point should land after the slide. The distance and direction between those two clicks become the vector, and the whole figure slides by that same amount. Check your result: the image should look identical to the original — same size, same shape, same orientation — just in a new position. Record the direction and distance of your translation (for example, "3 units right, 2 units up"). You will need this for your annotations and your Artist's Mathematical Statement. Part 4: Use the Rotation Tool A rotation turns your figure around a fixed point, called the center of rotation, through a specified angle and direction. Select the polygon you want to rotate. Open the Transform menu and choose Rotate. Desmos asks you to choose a center point. Click any point in your workspace — it can be a vertex of your figure, a point inside it, or a point somewhere else in the design. Your choice becomes part of your annotation, so pick it on purpose. Enter the angle of rotation and the direction (counterclockwise or clockwise). Common choices are 90° and 180°. Check your result: the image should be the same size and shape as the original, turned about the center point you chose. Mark the center of rotation clearly (for example, label it P) and note the angle and direction you used. ​ Virtual Pro-Tip: Screenshots for Your Submission Your final project is submitted digitally through Canvas, so plan your screenshots as you build — not as a scramble at the end. Take the screenshot. On a Windows laptop, press the Windows key + Shift + S, then drag a box around your design. On a Mac, press Command + Shift + 4, then drag a box around your design. On a Chromebook, press Shift + Ctrl + Show Windows (the key with a rectangle made of two lines), then drag a box. The screenshot saves to your clipboard or screenshots folder. Paste it into a Google Doc or slide so you can annotate it. Annotate it. In a Google Doc, use Insert → Drawing to insert the screenshot and to add labels using text boxes and arrows directly in the DRAW space along with any other requested transformation asks, In a Google Slide, use Insert → Image and insert text boxes and arrows directly on a slide to add labels and the other requested transformation asks. For each transformation, label the original figure, the image, and the feature the rubric asks for: the line of reflection, the translation's direction and distance, or the rotation's center, angle, and direction. Use one color of text or arrow per transformation so each example is easy to spot. Crop out empty workspace so the mathematical features fill the frame. Save as you go. Take a screenshot after each transformation you complete. If something goes wrong later in Desmos, you will still have evidence of the work you already finished. Quick Check Before You Build Your Full Design Before moving on to your full design, confirm you can do each of these in Desmos without looking back at the guide: Create a polygon and label its vertices. Reflect a figure and identify the line of reflection. Translate a figure and state the direction and distance. Rotate a figure and identify the center, angle, and direction. Take and annotate a screenshot of each transformation as you go. If any step feels shaky, re-read that part above and practice it once on a scratch polygon before you begin your final design using the individual transformations indicated in the screenshots.