Reflecting about Planes

Tim Brzezinski, Sep 29, 2020

Reflecting about Planes: Introductory explorations

Table of Contents

  1. Getting Started
    1. Reflecting about Planes: Introduction
  2. Reflecting about x = 0
    1. Reflecting about x = 0
  3. Reflecting about y = 0
    1. Reflecting about y = 0
  4. Reflecting about z = 0
    1. Reflecting about z = 0
  5. Reflecting about y = x
    1. Reflecting about y = x
  6. Reflecting about z = x
    1. Reflecting about z = x
  7. Reflecting about z = y
    1. Reflecting about z = y

1.

Getting Started

  • 1. Reflecting about Planes: Introduction

1.1.

Reflecting about Planes: Introduction

Interact with app below for a few minutes. The LARGE POINTS and sliders (left) are moveable.
What do you see going on here? What do you wonder? Notice anything interesting? If so, describe.
Is it possible to drag A, B, and C to make the gray plane (that contains them) disappear? Try to do so!
Were you able to make the plane disappear in the app above? If so, what causes this to happen? Describe.
Drag A, B, and C around so that the plane "looks" diagonal and so that O and O' are both visible. Then slide the SlideMe slider on the left.
What do you notice about O and its reflection O'? Describe as specifically best as you can.
Now drag point O [i]onto the plane itself[/i]. You may need to reposition the plane to do effectively do so. If point O lies on the plane, where does its reflection lie?
– Tim Brzezinski

2.

Reflecting about x = 0

  • 1. Reflecting about x = 0

2.1.

Reflecting about x = 0

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has an x-coordinate of 0. (This will cause the plane to have equation x = 0).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane x = 0?
– Tim Brzezinski

3.

Reflecting about y = 0

  • 1. Reflecting about y = 0

3.1.

Reflecting about y = 0

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has a y-coordinate of 0. (This will cause the plane to have equation y = 0).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane y = 0?
– Tim Brzezinski

4.

Reflecting about z = 0

  • 1. Reflecting about z = 0

4.1.

Reflecting about z = 0

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has a z-coordinate of 0. (This will cause the plane to have equation x = 0).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane z = 0?
– Tim Brzezinski

5.

Reflecting about y = x

  • 1. Reflecting about y = x

5.1.

Reflecting about y = x

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has both x and y coordinates equal to each other. (This will cause the plane to have equation y = x).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane y = x?
– Tim Brzezinski

6.

Reflecting about z = x

  • 1. Reflecting about z = x

6.1.

Reflecting about z = x

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has both z and x coordinates equal to each other. (This will cause the plane to have equation z = x).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane z = x?
– Tim Brzezinski

7.

Reflecting about z = y

  • 1. Reflecting about z = y

7.1.

Reflecting about z = y

Move A, B, and C around so that the plane DOES NOT DISAPPEAR and so that each of these points has both z and y coordinates equal to each other. (This will cause the plane to have equation z = y).
Drag O (preimage) to different positions. Record the coordinates of O in the PREIMAGE column. Record coordinates of its reflection in the plane in the IMAGE column.
What do you notice? Describe.
Suppose point O = (a, b, c). What would its image O' be if O was reflected about the plane z = y?
– Tim Brzezinski

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