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Translation-Reflection-and-Rotation-of-Shapes.pptx

In this lesson, we will explore how shapes move on a flat surface — without changing their size or shape. These movements are called geometric transformations.

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Translation, Reflection, and Rotation of Shapes Welcome to Week 2! In this lesson, we will explore how shapes move on a flat surface — without changing their size or shape. These movements are called geometric transformations. By the end of today, you'll be able to identify, describe, and draw the results of sliding, flipping, and turning any shape! GRADE 6 MATH WEEK 2 GEOMETRY
What Is a Geometric Transformation? A transformation is a movement or change in the position of a shape on a plane. The original shape is called the pre-image, and the shape after the movement is called the image. In all three transformations we study today, the shape stays congruent — same size, same shape, just in a new position! Translation Slide the shape to a new location — no turning, no flipping. Reflection Flip the shape over a line — like a mirror image. Rotation Turn the shape around a fixed point — like a clock hand. Key Idea: All three transformations preserve size and shape. The figures are always congruent before and after!
Translation — The Slide A translation moves every point of a shape the same distance in the same direction. Think of it as sliding a piece of paper across your desk — it doesn't spin or flip, it just moves! On a coordinate plane, we describe translations using directions: left, right, up, or down — and by how many units. How to Describe It Say: "The shape moves 3 units right and 2 units up." Every vertex (corner) moves the exact same way! Example on a Grid If point A is at (1, 2) and we translate it 4 units right and 1 unit down, it lands at (5, 1). Just add or subtract from the coordinates! • Right add to x-coordinate → • Left subtract from x-coordinate → • Up add to y-coordinate → • Down subtract from y-coordinate →
Translation in Action Let's see translation step by step. We move a triangle 5 units to the right and 3 units up on the coordinate plane. Every single corner of the triangle makes the exact same move! Plot & Connect Translate Coordinates Identify Shape Practice tip: Always move every vertex by the same amount. Then connect the dots to reveal your translated image. If your new shape looks exactly like the original, you did it right! Remember: A translated shape is congruent to the original — same size, same shape, just in a new spot on the grid!
Reflection — The Flip A reflection flips a shape over a special line called the line of reflection. The result looks like a mirror image — like holding a shape up to a mirror! The shape is the same distance from the line on both sides, but it faces the opposite direction. Reflect Over the Y-Axis The y-axis is a vertical mirror. Each point (x, y) becomes ( x, y) − . The shape flips left to right. Reflect Over the X-Axis The x-axis is a horizontal mirror. Each point (x, y) becomes (x, y) − . The shape flips up to down. Reflect Over Any Line You can flip over any line — the key is that each point lands the same distance from the line on the other side.
Reflection — Key Rules to Remember Step-by-Step: How to Reflect a Shape 1. Identify the line of reflection (x-axis, y-axis, or another line) 2. Find each vertex (corner) of the original shape 3. Count the distance from each vertex to the mirror line 4. Plot the new vertex the same distance on the opposite side 5. Connect the new vertices to form the reflected image The line of reflection acts like a fold line. If you folded the paper along it, the two shapes would match up perfectly! Quick Reference Over y-axis: (x, y) ( x, y) → − Over x-axis: (x, y) (x, y) → − Over y = x: (x, y) (y, x) → The line of reflection is always equidistant from both the image and the pre-image.
Rotation — The Turn A rotation turns a shape around a fixed point called the center of rotation. Think of a clock hand spinning around the center — every point on the hand moves, but they all stay the same distance from the middle. We describe rotations by their angle and direction. 1 90° Clockwise A quarter turn to the right. Point (x, y) becomes (y, x) − . 2 180° Turn A half turn — upside down! Point (x, y) becomes ( x, y) − − . Same result clockwise or counterclockwise. 3 90° Counterclockwise A quarter turn to the left. Point (x, y) becomes ( y, x) − . 4 360° Full Turn One complete rotation brings the shape back to its original position!
Comparing All Three Transformations Now let's put it all together! Here's a side-by-side look at how each transformation moves a shape — and what makes each one unique. All three keep the shape congruent, but they each do something different to its position or orientation. Feature Translation (Slide) Reflection (Flip) Rotation (Turn) Motion Type Slides in one direction Flips over a line Turns around a point Key Reference Direction + distance Line of reflection Center + angle + direction Orientation Same as original Reversed (mirror) Changed by angle Shape & Size Unchanged ✓ Unchanged ✓ Unchanged ✓ Everyday Example Sliding a book Mirror reflection Spinning a top All transformations produce a congruent image — the shape is always the same size and shape as the original!
Transformations on the Coordinate Plane The coordinate plane is our map for transformations! Using ordered pairs (x, y), we can describe exactly where a shape starts and where it ends up after a transformation. Let's practice with a triangle that has vertices at A(1, 1), B(3, 1), and C(2, 4). Using coordinates makes transformations precise and repeatable. Every point follows the same rule — and you can always check your work by counting units on the grid!
Key Takeaways & What's Next Great work today! You've learned how shapes move on the coordinate plane using three powerful transformations. Remember: the shape never changes size — only its position or direction does! Translation = Slide Move every point the same distance in the same direction. Use coordinates to add or subtract units. Reflection = Flip Flip the shape over a line of reflection. The image is a mirror of the original, equidistant from the line. Rotation = Turn Turn the shape around a center point. Describe the angle (90°, 180°, 270°) and direction (clockwise or counterclockwise). 🌟 Coming Up: In our next lesson, we'll practice drawing transformations on the coordinate plane and explore how shapes can have symmetry through reflections. Get your graph paper ready!