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Enlargement: Scale, Centre, Vertices, Invariant Points

Learn about the concept of enlargements in 2D shapes, including scale factor, centre of enlargement, and invariant points. Explore the properties and transformations of enlarged shapes.

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Enlargement: Scale, Centre, Vertices, Invariant Points

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  1. Two transformations are applied to a hexagon. The result is shown. Describe a pair of possible transformations. And another….. And another….

  2. Plot the coordinates, join them up and label the vertices A D C B A:(6,6) B:(6,3) C:(12,3) D:(12,6) You should have a rectangle.

  3. A D Can you include these words in your discussion? Scale Vertices Centre Angles Congruent A’ D’ C B C’ B’ What can we say about the new shape? A:(6,6) B:(6,3) C:(12,3) D:(12,6) Label the new vertices A’, B’, C’ and D’

  4. A D A’ D’ C B C’ B’ The centre of enlargement is (0,0)

  5. A D “DON’T RUB ME OFF” A’ D’ C B C’ B’ The centre of enlargement is (0,0)

  6. A D What is the same? What is different? Can you include these words in your discussion? Scale Centre Vertices Intersect C B A’ D’ B’ C’ A:(6,6) B:(6,3) C:(12,3) D:(12,6) Label the new vertices A’, B’, C’ and D’

  7. A D Counting squares to check C B A’ D’ B’ C’ A:(6,6) B:(6,3) C:(12,3) D:(12,6) Label the new vertices A’, B’, C’ and D’

  8. Draw the two shapes and label the vertices Shape 1 A(-9,6) B:(-9,2) C:(-5,2) D:(-5, 6) Shape 2 A’: (-9,1) B’:(-9,-1) C’:(-7, -1) D’:(-7, 1) A D Describe the transformation “DON’T RUB ME OFF” B C A’ D’ B’ C’

  9. Draw the two shapes and label the vertices Shape 1 A(-9,6) B:(-9,2) C:(-5,2) D:(-5, 6) Shape 2 A’:(-8,5) B’:(-8,3) C’:(-6,3) D’:(-6,5) A D Describe the transformation A’ D’ C’ B’ B C

  10. Draw the two shapes and label the vertices Shape 1 A(-9,6) B:(-9,2) C:(-5,2) D:(-5, 6) Shape 2 A’:(-9,5) B’:(-9,2) C’:(-6,2) D’:(-6,5) A D Describe the transformation D’ A’ Notice how B = B’ This point is a fixed point and is called an INVARIANT point. C’ B C

  11. Title: Enlargement • To enlarge a 2D shape, two pieces of information are required: • Scale Factor • Centre of Enlargement • The scale factor describes how much bigger or smaller the enlarged image is to be. • The centre of enlargement determines where the enlarged image will be drawn. • Enlarged images are not the same size, therefore they are not congruent. • Invariant points are points that do not move when they are transformed.

  12. Your Turn: Where is the centre of enlargement?

  13. Your Turn: Copy each diagram in your book and enlarge the triangles by a SF of 2 using the centre of enlargement marked.

  14. Challenge Draw the enlargements in your book, scale factor 2, with centre shown

  15. Always true, sometimes true or never true? Enlargements increase the size of a shape.

  16. Always true, sometimes true or never true? Using a fractional scale factor will result in a smaller shape

  17. Always true, sometimes true or never true? For an enlargement to create an invariant point the centre of enlargement must also be a vertex.

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