Geometry and measuresHigher

Enlargements - positive and negative fractional scale factors

Compare positive and negative fractional scale factors.

  • When the image is smaller. The transformation is still called an enlargement.
  • A positive fraction keeps the image on the same side of the centre. A negative fraction puts it on the opposite side.
  • Scale both components of the displacement from the centre, then add the centre back.

Example 1

Enlarge triangle with centre and scale factor . Draw and label the image.

  1. Start at the centre

    Draw a line from through each vertex.

  2. Multiply the displacement

    Multiply both components of the vector from the centre by . A positive factor keeps the image on the same side of the centre.

  3. Plot the image

    Add the new displacement to the centre. The image is smaller because .

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction
  • For : start with displacement . Multiply by to get , then add it to the centre.

Example 2

Enlarge triangle with centre and scale factor . Draw and label the image.

  1. Start at the centre

    Draw a line from through each vertex.

  2. Multiply the displacement

    Multiply both components of the vector from the centre by . A negative factor places the image on the opposite side of the centre.

  3. Plot the image

    Add the new displacement to the centre. The image is smaller because .

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction
  • For : start with displacement . Multiply by to get , then add it to the centre.

Remember
Use corresponding vertices to check the whole shape, not just one side.

Your turn

Question 1

Enlarge triangle with centre and scale factor . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 2

Enlarge triangle with centre and scale factor . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 3

Enlarge triangle with centre and scale factor . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 4

Enlarge triangle with centre and scale factor . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 5

Enlarge triangle with centre and scale factor . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

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