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Module 7 (M7) - Geometry and measures - Transformations

Part of MathsM7: Geometry and measures

Transformations

It may be useful to look at M5 Transformations and M6 Transformations

Transformations change the size or position of shapes.
Scale factors can change the size of shapes.

The 4 transformations of 2D shapes:

  • Translation - moving a shape in a straight line
  • Reflection - flipping a shape to create a mirror image
  • Rotation - turning a shape
  • Enlargement - changing the size of a shape by a scale factor

It is important to know how to draw and/or describe transformations

M7 transformations looks at

  • Reflection - in a diagonal line
  • Enlargement - using a fractional scale factor
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Reflection in a diagonal line

To reflect a shape in a diagonal line
Triangle reflected in a diagonal line
  1. Draw the line of reflection.
  2. From a point on the shape, count how far it is vertically from the line of reflection.
  3. Count the same amount horizontally on the other side of the line and plot the point.
  4. Repeat steps 2 and 3 for each point in the shape.

It is important to know the names of the diagonal lines.

The positive diagonal is y = x
The negative diagonal is y = -x

Question

Reflect the shape in the line y = x

Triangle ABC on a set of co-ordinates

Question

Describe the transformation of the shape ABC.

Triangle (ABC) reflected in the line, y=-x

Remember



There will be a mark for writing reflection and a mark for writing in the line \(y = - x\)

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Enlargement with a fractional scale factor

When a shape is enlarged by a between 0 and 1, the image is smaller than the original shape.

The triangle ABC is enlarged by a scale factor of â…“. All the sides of triangle A'B'C' are one third as long as the sides of the original triangle ABC.

Triangle (ABC) is enlarged by 1/3 to triangle A'B'C'

Example

Enlarge the triangle ABC by a scale factor of ½ about the centre of enlargement O.

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  1. Enlarge triangle (ABC) by 1/2

    First, draw ray lines from O to each corner of the triangle.

Alternatively these distances can be shown as vectors. \(\text{OA} = \left( \matrix{ 2 \cr 2 \cr} \right)\) so under a scale factor of ½ , \(\text{OA'} = \left( \matrix{ 1 \cr 1 \cr} \right)\).

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Finding the centre of enlargement

To find the centre of enlargement, draw ray lines from the corners of the image through the corners of the original shape.

Example

Describe the transformation of the triangle RST.

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  1. Triangles (STR) and (S'T'R') with lines of enlargement

    Draw ray lines from the corners of triangle RST through the corners of R'S'T' until they cross. This is the centre of enlargement

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Test yourself

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More on M7: Geometry and measures

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