Enlargement: fractional scale factors

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  1. P (4, 3) is enlarged by scale factor 2, centre (2, 1). Find the coordinates of P′.

    P′ (6, 5)

  2. P (2, 5) is enlarged by scale factor 3, centre (3, 4). Find the coordinates of P′.

    P′ (0, 7)

  3. P (−1, 2) is enlarged by scale factor 2, centre (1, −1). Find the coordinates of P′.

    P′ (−3, 5)

Does an enlargement always
make a shape bigger?

No

Bigger or smaller?

Scale factor ¼ Smaller

How long is the new side?

12 cm, scale factor ½ 6 cm

  1. A 20 cm side is enlarged by scale factor ¼. How long is the new side?

    5 cm

  2. A shape is enlarged by scale factor ¾. Is the image bigger or smaller than the shape?

    Smaller

  3. A 6 cm side becomes 3 cm. What is the scale factor?

    ½

  4. After an enlargement by scale factor ½, a side is 4 cm. How long was it before?

    8 cm

Enlarge the shape by scale factor ½ about C (−2, −1).

−3−2−112345−2−11234560CPQR
VertexJourney from CJourney × ½Image vertex
P (2, 1)right 4, up 2right 2, up 1P′ (0, 0)
Q (4, 1)right 6, up 2right 3, up 1Q′ (1, 0)
R (2, 5)right 4, up 6right 2, up 3R′ (0, 2)

Enlarge the shape by scale factor ⅓ about C (0, 0).

−11234567−112345670CPQRS
VertexJourney from CJourney × ⅓Image vertex
P (3, 3)right 3, up 3right 1, up 1P′ (1, 1)
Q (6, 3)right 6, up 3right 2, up 1Q′ (2, 1)
R (6, 6)right 6, up 6right 2, up 2R′ (2, 2)
S (3, 6)right 3, up 6right 1, up 2S′ (1, 2)

Enlarge the shape by scale factor ½ about C (−2, −1).

−3−2−112345−2−11234560CPQR
VertexJourney from CJourney × ½Image vertex
P (2, 1)right 4, up 2right 2, up 1P′ (0, 0)
Q (4, 1)right 6, up 2right 3, up 1Q′ (1, 0)
R (2, 5)right 4, up 6right 2, up 3R′ (0, 2)

Enlarge the shape by scale factor ½ about C (1, −2).

−11234567−3−2−1123450CPQR
VertexJourney from CJourney × ½Image vertex
P (5, 0)right 4, up 2right 2, up 1P′ (3, −1)
Q (5, 4)right 4, up 6right 2, up 3Q′ (3, 1)
R (3, 0)right 2, up 2right 1, up 1R′ (2, −1)

Enlarge the shape by scale factor ½ about C (−2, −1).

−3−2−112345−2−11234560CPQR
VertexJourney from CJourney × ½Image vertex
P (2, 1)right 4, up 2right 2, up 1P′ (0, 0)
Q (4, 1)right 6, up 2right 3, up 1Q′ (1, 0)
R (2, 5)right 4, up 6right 2, up 3R′ (0, 2)

Enlarge the shape by scale factor ½ about C (7, 5).

123456781234560CPQR
VertexJourney from CJourney × ½Image vertex
P (1, 1)left 6, down 4left 3, down 2P′ (4, 3)
Q (5, 1)left 2, down 4left 1, down 2Q′ (6, 3)
R (1, 3)left 6, down 2left 3, down 1R′ (4, 4)

Enlarge the shape by scale factor ½ about C (−2, −1).

−3−2−112345−2−11234560CPQR
VertexJourney from CJourney × ½Image vertex
P (2, 1)right 4, up 2right 2, up 1P′ (0, 0)
Q (4, 1)right 6, up 2right 3, up 1Q′ (1, 0)
R (2, 5)right 4, up 6right 2, up 3R′ (0, 2)

Enlarge the shape by scale factor ⅓ about C (−1, −2).

−2−1123456−3−2−1123450CPQR
VertexJourney from CJourney × ⅓Image vertex
P (2, 1)right 3, up 3right 1, up 1P′ (0, −1)
Q (5, 1)right 6, up 3right 2, up 1Q′ (1, −1)
R (2, 4)right 3, up 6right 1, up 2R′ (0, 0)

Enlarge the shape by scale factor ½ about C (−2, −1).

−3−2−112345−2−11234560CPQR
VertexJourney from CJourney × ½Image vertex
P (2, 1)right 4, up 2right 2, up 1P′ (0, 0)
Q (4, 1)right 6, up 2right 3, up 1Q′ (1, 0)
R (2, 5)right 4, up 6right 2, up 3R′ (0, 2)

Enlarge the shape by scale factor ½ about C (3, 3).

−1123456−11234560CPQRS
VertexJourney from CJourney × ½Image vertex
P (1, 1)left 2, down 2left 1, down 1P′ (2, 2)
Q (5, 1)right 2, down 2right 1, down 1Q′ (4, 2)
R (5, 5)right 2, up 2right 1, up 1R′ (4, 4)
S (1, 5)left 2, up 2left 1, up 1S′ (2, 4)

Enlargement: integer and fractional scale factors worksheet, page 1

Answer sheet

  1. An enlargement turns a 12 cm side into a 9 cm side. What is the scale factor?

    ¾

  2. A shape is enlarged by scale factor 3, then by scale factor ⅓. What size is it now?

    The size it started

  1. A 15 cm side is enlarged by scale factor 13. How long is the new side?

    5 cm

  2. Enlarge shape A by scale factor 12, centre C. (Draw it on your ticket.)

    AC

  3. After an enlargement by scale factor 34, a side is 9 cm. How long was it before?

    12 cm
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