Topic 10: Reflection

By the end of this topic, you will be able to:

• identify lines of symmetry for different figures
• reflect shapes and objects
• apply reflection in the cartesian plane

Keywords

• cartesian
• data
• grid
• image
• object
• plane
• reflection
• shape
• symmetry

Introduction

The image of an object after reflection is its mirror image in the axis or plane of reflection. For example, when you reflect 6 in the vertical axis iso. In this topic, you will learn how to identify the lines of symmetry, state the properties of reflection as a transformation, make geometrical deductions and apply reflection in the Cartesian plane.

Identifying lines of Symmetry for Different Figures

When we divide figures, shape, letters of alphabet as capital letters, numbers and many others into halves and they look similar, we say a line of symmetry has been created. There may be more than one line of symmetry.

Activity 10.1 Identifying and drawing lines of symmetry (work in pairs)

What you need: ink, pen, paper, note book.

What to do:

1. Fold a piece of paper in half.

2. Open the paper and put in one drop of ink on the fold

3. Close the paper over the ink and press down hard on the paper.

4. Open the paper, when the ink is dry.

5. Look at both sides of the fold line. Are they the same size and shape?

6. Record your observation about the size and shape.

7. Draw a line joining two corresponding points on the ink marks. What is the angle between the line and the fold?

8. Present your work to the whole class.

Examples (Discuss in groups)

Identify the lines of symmetry of the shapes below.

3. Identify and draw the lines of symmetry in the first 10 whole numbers.

Reflecting Shapes and Objects

When you look through a mirror, your image is the same distance from the mirror as you are.

Similarly, when a shape or other object is reflected through a line, the image is the same distance from the mirror line as the object. In the following activity, you will reflect shapes and objects.

Activity 10.2 Reflecting shapes and objects (work in groups)

What you need: objects, shapes, a mirror a note book and a pen.

What to do:

1. Draw a line PR.

2. Place a mirror along line AB as shown.

3. Place one of the shapes in front of the mirror and observe the orientation of the image.

4. Remove the mirror, trace the outline of the object and draw a line perpendicular to the mirror line from each vertex as shown above.

5. Extend line AR, CQ and BP to determine the vertices of the image A’B’C’ AR = RA’, CQ = QC’ and BP = PB’.

Applying reflection in a Cartesian plane

You can use the Cartesian plane accurately determine the size I shape of the image and its ance from different lines of semetry.

Activity 10.3 Applying reflection in a Cartesian plane (work in groups)

what you need: a graph paper, pen, ruler and pencil. at to do:

1. Draw the Cartesian plane and plot A(1, 1), B(4, 2) and C(2, 4).
2. Join the points to form a figure.
3. Use the x-axis as the line of reflection, use dotted lines to find the perpendicular distances of vertices A, B and C from the x-axis. Label the points of intersection as P, Q and R respectively.
4. Extend the dotted lines to determine the vertices of the image A’B’C’ such that AP = PA’, BQ = QB’ and CR = RC.
5. Connect the points A’, B’ and C’ to form the image.
6. Repeat the steps above using the following lines of reflection.
   • a) y-axis b) Line y = x c) Line y = -x Compare your answer with that of other group members.

Exercise 10.2

1. After a reflection, the images of A (2, 3), B(-3, 3), C(0, 5) and D are A'(3,2), B'(3, -3), C'(5, 0) and D'(5, 3).

a) Plot the coordinates of ABC and D and its image on the same Cartesian plane. b) Determine the line of reflection.

2. Plot the triangle ABC for which A(-4, 1), B(-2, 1) and C(-3, 3). Reflect triangle ABC in a line y = x. State the co-ordinates of A’, B’ and C’.

3. Plot the points A(-4, -3), B(-1, -3) and C(-2,-1) on the Cartesian plane. Join the points to create the object. After the reflection, the image has points A'(3, 4), B'(3,1) and C'(1, 2). Dro the line of reflection.