Transformations

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.

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 B C D A’ B’ C’ D’ objectimage mirror line or axis of reflection The image is congruent to the original shape.

A B C D A’ B’ C’ D’ objectimage mirror line or axis of reflection 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.

Reflecting shapes

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Finding a line of reflection Construct the line that reflects shape A onto its image A’. A’ A This is the line of reflection. Draw lines from any two vertices to their images. Draw a line through the mid points. Mark on the mid-point of each line.

Reflection on X-axis

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07/12/2015Reflections13 Example 1

Reflection on Y-axis

Reflecting shapes

Reflect this shape

07/12/2015Reflections17 1. Reflect this triangle in the y-axis Reflect the shape in a mirror line

07/12/2015Reflections18 1. Reflect this triangle in the y-axis 2. Draw lines from each vertex (corner) at 90 0 to the mirror line (y- axis)

07/12/2015Reflections19 1. Reflect this triangle in the y-axis 2. Draw lines from each vertex (corner) at 90 0 to the mirror line (y- axis) 3. Use these lines to find the reflected points

07/12/2015Reflections20 1. Reflect this triangle in the y-axis 2. Draw lines from each vertex (corner) at 90 0 to the mirror line (y- axis) 3. Use these lines to find the reflected points 4. Draw the reflection

07/12/2015Reflections21 Example

Reflection on the line Y =X

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Reflection on the line Y = -X

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Reflection on the line x = h

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Reflection on the line y = k

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Reflection Summary Reflection on X-axis: P(x, y) P’(x, -y) Reflection on Y-axis: P(x, y) P’(-x, y) Reflection on y= x: P(x, y) P’(y, x) Reflection on y = - x: P(x, y) P’(-y, -x) Reflection on x = h: P(x, y) P’(2h-x, y) Reflection on y = k: P(x, y) P’(x, 2k-y) Note: X-axis means y = 0 Y-axis means x = 0 Line parallel to X-axis means y = k Line parallel to Y-axis means x = h

Reflect this shape

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

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

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

Reflect this shape

Reflection on a coordinate grid

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

e.g.

Reflect the object shape in the mirror line shown. Trace the shape and mirror line using tracing paper. Turn tracing paper over and match up mirror lines/square corners. Mirror Line object image Mark position of vertices, remove tracing paper and draw image of shape. Reflections Using Tracing Paper

Tracing 1 Reflections Using Tracing Paper object Mirror Line Reflect the object shape in the mirror line shown. Trace the shape and mirror line using tracing paper. Turn tracing paper over and match up mirror lines.

object Mirror Line Reflect the shape in the mirror line shown. Trace the shape and mirror line using tracing paper. Turn tracing paper over and match up mirror lines. Mark position of vertices, remove tracing paper and draw image of shape. Reflections Using Tracing Paper

Mirror Line Reflect the shape in the mirror line shown. Trace the shape and mirror line using tracing paper. Turn tracing paper over and match up mirror lines. Mark position of vertices, remove tracing paper and draw image of shape. object image Reflections Using Tracing Paper

Tracing 2 Mirror Line Reflect the object shape in the mirror line shown. Trace the shape and mirror line using tracing paper. object Turn tracing paper over and match up mirror lines. Reflections Using Tracing Paper

Mirror Line Reflect the object shape in the mirror line shown. Trace the shape and mirror line using tracing paper. object Turn tracing paper over and match up mirror lines. Mark position of vertices, remove tracing paper and draw image of shape. Reflections Using Tracing Paper

Mirror Line Reflect the object shape in the mirror line shown. Trace the shape and mirror line using tracing paper. object Turn tracing paper over and match up mirror lines. Mark position of vertices, remove tracing paper and draw image of shape. image Reflections Using Tracing Paper