Geometry and measuresHigher

Enlargements - negative scale factors

Place the image on the opposite side of the centre.

  • A negative scale factor reverses each displacement vector through the centre.
  • Distances from the centre are multiplied by .
  • For the image is the same size, equivalent to a rotation about the centre.

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 negative factor places the image on the opposite side of the centre.

  3. Plot the image

    Add the new displacement to the centre. Corresponding lengths are multiplied by .

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. Corresponding lengths are multiplied by .

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.

← All Geometry and measures cardsReport a mistake