Reflection An object can be reflected in a

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.

Reflecting shapes If we reflect the quadrilateral ABCD in a mirror line we label the image quadrilateral A’B’C’D’. A A’ B B’ object image C’ C D 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’ A B’ B object image C’ C D D’ mirror line or axis of reflection

Reflecting shapes

The line of reflection is the perpendicular bisector of the segment joining every point and its image. NOTATION :

Reflecting shapes by folding paper We can make reflections by folding paper. Draw a random polygon at the top of a piece of paper. Fold the piece of paper back on itself so you can still see the shape. Pierce through each vertex of the shape using a compass point. When the paper is unfolded the vertices of the image will be visible. Join the vertices together using a ruler.

Reflecting shapes using tracing paper Suppose we want to reflect this shape in the given mirror line. Use a piece of tracing paper to carefully trace over the shape and the mirror line with a soft pencil. When you turn the tracing paper over you will see the following: Place the tracing paper over the original image making sure the symmetry lines coincide. Draw around the outline on the back of the tracing paper to trace the image onto the original piece of paper.

Reflect this shape

Reflection on a coordinate grid y A’(– 2, 6) 7 B’(– 7, 3) 6 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 – 1 C’(– 4, – 1) – 2 – 3 – 4 – 5 – 6 – 7 A(2, 6) B(7, 3) 1 2 3 4 5 6 7 x C(4, – 1) The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, – 1). Reflect the triangle in the y-axis and label each point on the image. What do you notice about each point and its image?

Reflection on a coordinate grid y A(– 4, 6) D(– 5, 3) 7 6 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 – 1 D’(– 5, – 3) – 2 – 3 – 4 – 5 – 6 – 7 A’(– 4, – 6) B(4, 5) C(2, – 2) 1 2 3 4 5 6 7 x C’(2, – 2) B’(4, – 5) The vertices of a quadrilateral lie on the points A(– 4, 6), B(4, 5), C(2, – 2) and D(– 5, 3). Reflect the quadrilateral in the x-axis and label each point on the image. What do you notice about each point and its image?

Reflection on a coordinate grid B’(– 1, 7) C’(– 6, 2) y 7 6 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 – 5 – 6 – 7 x=y A’(4, 4) A(4, 4) 1 2 3 4 5 6 7 x B(7, – 1) C(2, – 6) The vertices of a triangle lie on the points A(4, 4), B(7, – 1) and C(2, – 6). Reflect the triangle in the line y = x and label each point on the image. What do you notice about each point and its image?