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Exploring Reflections - Unit 7 AAC

Author:Lynn Martineau, leeb, John Williams
Exploring Reflections

Directions

1. Click on ORIGINAL. The original shape is known as the pre-image. You will see a shape, the vertices, and the ordered pair for each vertex. Drag any of the original points (A, B, C, D, E) to create your own original shape. Keep the points on whole numbers ( (3, -1) instead of (2.97, -.98)) 2. Click the box that says REFLECT. Your reflected shape is called the image. 3. Click on the box that says MIRROR LINE Now that you have a mirror line, move the points on the line around the coordinate plane, which will move your reflected image also. You will reflect your pre-image over the x-axis, the y-axis, y = x, y = -x, and three other lines. Use the spreadsheet in Google Classroom to keep track of how each mirror line changes the coordinates of the image.

Reflections over any line

Is the distance of the original point and the new point from the mirror line the same? Or different?

Reflections over the x-axis

When you reflect over the x-axis, what do you notice about the original point(s) and the reflected point(s)?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Reflections over the y-axis

When you reflect over the y-axis, what do you notice about the original point(s) and the reflected point(s)?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Reflections over a diagonal, pt 1

Create a diagonal mirror line that shows a positive slope through the origin. Move the points so that when y = 1, x = 1, and when y = -2, x = -2. This is the mirror line y = x. What do you notice about the original point(s) and the reflected point(s)?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Reflections over a diagonal, pt 2

Create a diagonal mirror line that shows a positive slope through the origin. Move the points so that when y = 1, x = -1, and when y = 2, x = -2. This is the mirror line y = -x. What do you notice about the original point(s) and the reflected point(s)?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Reflections over other lines...

What is your mirror line isn't an x- or y-axis, or y = x? Create 3 reflections using the following lines: y = x - 3 y = -2x + 1 How do the points change? Now move your reflection line so that it is a horizontal line that isn't the x-axis (y = -1) Then do it again so that your reflection line is a vertical line that isn't the y-axis (x = -1). How do the points change? Is there a mathematical relationship between the original points and the reflected points? Can you create a rule that explains what happens if your line of reflection isn't on an axis?

Line of Reflection

For reflections, the line of reflection is the perpendicular bisector of the segments that connect each preimage point to the corresponding point on the image. 1. Using the segment tool, create a line segment from each point on the preimage to its corresponding point on the image 2. Using the perpendicular bisector tool, create the line of reflection. Change the image, move it around, and do it again! (Practice makes perfect)

Ticket out the Door

Why is a reflection considered a rigid transformation? What is the relationship between each original point, its reflection, and the mirror line?

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