Enlargement: negative scale factors

The Maths Habit

Scale factor 2 doubles every journey from the centre. What could scale factor −1 do?

Send every point the same distance the other way through the centre

Enlarge A by scale factor −1, centre (0, 0). P′ (−3, −1)

−4−3−2−11234−3−2−11230APBP′

Enlarge A by scale factor −2, centre (0, 0). P′ (−4, −4)

−5−4−3−2−1123−5−4−3−2−11230APBP′

Enlarge A by scale factor −1, centre (0, 0). P′ (−3, −1)

−4−3−2−11234−3−2−11230APBP′

Enlarge A by scale factor −12, centre (0, 0). P′ (−2, −1)

−3−2−112345−3−2−1123450APBP′

Enlarge A by scale factor −1, centre (0, 0). P′ (−3, −1)

−4−3−2−11234−3−2−11230APBP′

Enlarge A by scale factor −2, centre (0, 0). P′ (2, −2)

−4−3−2−11234−4−3−2−11230ACB

Enlarge A by scale factor −1, centre (0, 0). P′ (−3, −1)

−4−3−2−11234−3−2−11230APBP′

Enlarge A by scale factor −1, centre (0, 0). P′ (−4, 1)

−4−3−2−11234−3−2−11230ACB

Enlarge A by scale factor −1, centre (0, 0). P′ (−3, −1)

−4−3−2−11234−3−2−11230APBP′

Enlarge A by scale factor −3, centre (0, 0). P′ (−3, −3)

−6−5−4−3−2−112−6−5−4−3−2−1120ACB

Enlargement: negative scale factors worksheet, page 1

Answer sheet

  1. An enlargement, centre (0, 0), maps (9, 6) to (−3, −2). Find the scale factor.

    −13

  2. Which rotation gives the same image as an enlargement of scale factor −1?

    180° about the centre

  3. An enlargement of scale factor −12 sends P (5, 2) to P′ (−1, −1). Find the centre.

    (1, 0)

  1. P (3, −5) is enlarged by scale factor −1, centre (0, 0). Find the coordinates of P′.

    (−3, 5)

  2. Enlarge shape A by scale factor −2, centre C. (Draw it on your ticket.)

    AC

  3. An enlargement, centre (0, 0), maps (4, −2) to (−2, 1). Find the scale factor.

    −12
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