Reflections

2 Min Task: Draw the following shape and find how many lines of symmetry this shape has. 1 2 More than 2

Observe carefully! This shape has 2 lines of symmetry. Remember that the line of symmetry divides the whole object into two identical parts and each part lie on the opposite sides of the line of symmetry!

Reflections

Objectives To reflect an object in a mirror line. Keywords: Mirror line, object, image, line of reflection, axis of reflection

Reflections

Reflection An object can be reflected in a mirror line or axis of reflection to produce an image of the object. For example, Image Object Mirror Line Each point in the image must be the same distance from the mirror line as the corresponding point of the original object.

Reflection An object can be reflected in a mirror line or axis of reflection to produce an image of the object. For example, Each point in the image must be the same distance from the mirror line as the corresponding point of the original object.

The image is congruent to the original shape. Reflecting shapes If we reflect the quadrilateral ABCD in a mirror line we label the image quadrilateral A’B’C’D’. A B C D A’ B’ object image C’ Explain that we call the original shape the object and the reflected shape the image. The image of an object can be produced by any transformation including rotations, translations and enlargements, as well as reflections. Define the word congruent to mean the same shape and size. Link: S2 2-D shapes – congruence. D’ mirror line or axis of reflection The image is congruent to the original shape.

Reflecting shapes If we draw a line from any point on the object to its image the line forms a perpendicular bisector to the mirror line. A B C D A’ B’ C’ D’ object image mirror line or axis of reflection Stress that the mirror line is always perpendicular (at right angles) to any line connecting a point to its image. The mirror line also bisects the line (divides it into two equal parts).

Finding a line of reflection Construct the line that reflects shape A onto its image A’. A’ This is the line of reflection. A Two lines are sufficient to define the line of reflection. A third line can be used to check the position of the line. The mid-point can be found using a ruler to measure the length of the line, and then halving it. Draw lines from any two vertices to their images. Mark on the mid-point of each line. Draw a line through the mid points.

Reflection on a coordinate grid y The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1). A’(–2, 6) 7 A(2, 6) 6 B’(–7, 3) 5 B(7, 3) 4 3 2 Reflect the triangle in the y-axis and label each point on the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1 C’(–4, –1) –2 C(4, –1) –3 Pupils should notice that when a shape is reflected in the y-axis, the x-coordinate of each image point is the same as the x-coordinate of the original point × –1 and the y-coordinate of the image point is the same as the y-coordinate of the original point. In other words, the x-coordinate changes sign and the y-coordinate stays the same. –4 What do you notice about each point and its image? –5 –6 –7

Reflection on a coordinate grid y The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1). A’(–2, 6) 7 A(2, 6) 6 B’(–7, 3) 5 B(7, 3) 4 3 2 Reflect the triangle in the y-axis and label each point on the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1 C’(–4, –1) –2 C(4, –1) –3 Pupils should notice that when a shape is reflected in the y-axis, the x-coordinate of each image point is the same as the x-coordinate of the original point × –1 and the y-coordinate of the image point is the same as the y-coordinate of the original point. In other words, the x-coordinate changes sign and the y-coordinate stays the same. –4 What do you notice about each point and its image? –5 –6 –7

Reflection on a coordinate grid y The vertices of a quadrilateral lie on the points A(–4, 6), B(4, 5), C(2, 0) and D(–5, 3). A(–4, 6) 7 6 B(4, 5) 5 4 3 D(–5, 3) 2 1 C(2, 0) Reflect the quadrilateral in the x-axis and label each point on the image. –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1 C’(2, 0) D’(–5, –3) –2 –3 Pupils should notice that when a shape is reflected in the x-axis, the x-coordinate of each image point is the same as the x-coordinate of the original point and the y-coordinate of the image point is the same as the y-coordinate of the original point × –1. In other words, the x-coordinate stays the same and the y-coordinate changes sign. –4 What do you notice about each point and its image? –5 B’(4, –5) –6 A’(–4, –6) –7

Reflection on a coordinate grid y x = y B’(–1, 7) The vertices of a triangle lie on the points A(4, 4), B(7, –1) and C(2, –6). 7 6 A’(4, 4) 5 4 A(4, 4) 3 2 C’(–6, 2) Reflect the triangle in the line y = x and label each point on the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 B(7, –1) x –1 –2 –3 Pupils should notice that when a shape is reflected in the line x = y, the x-coordinate of each image point is the same as the y-coordinate of the original point and the y-coordinate of the image point is the same as the x-coordinate of the original point. In other words, the x- and y-coordinates are swapped around. –4 What do you notice about each point and its image? –5 –6 –7 C(2, –6)

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?

What letter would you get if you reflected each shape in its corresponding mirror line?