Lesson Worksheet: Dilation: Negative Scale Factors Mathematics

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In this worksheet, we will practice dilating shapes about a center of dilation by negative scale factors, fractional numbers, and whole numbers, and we will practice describing dilations.

Q1:

If triangle 𝐴′𝐵′𝐶′ is the image of triangle 𝐴𝐵𝐶 after a dilation from the origin, find the scale factor of this dilation.

Q2:

Which shape in the following figure is the image of shape 𝐴 after a dilation with a negative scale factor from the origin?

  • A𝐹
  • B𝐸
  • C𝐷
  • D𝐵
  • E𝐶

Q3:

Find the vertices of the image of kite 𝐴𝐵𝐶𝐷 after a dilation with scale factor −12 from the origin.

  • A𝐴(8,−4), 𝐵(4,−6), 𝐶(2,−4), 𝐷(4,−2)
  • B𝐴(−4,−2), 𝐵(−2,−3), 𝐶(−1,−2), 𝐷(−2,−1)
  • C𝐴(−4,−4), 𝐵(−2,−6), 𝐶(−1,−4), 𝐷(−2,−2)
  • D𝐴(4,2), 𝐵(2,3), 𝐶(1,2), 𝐷(2,1)
  • E𝐴(−4,2), 𝐵(−2,3), 𝐶(−1,2), 𝐷(−2,1)

Q4:

If shape 𝐵 is the image of shape 𝐴 after a dilation from the origin, find the scale factor of this dilation.

  • A2
  • B−12
  • C−4
  • D12
  • E−2

Q5:

Find the vertices of the image of triangle 𝐴𝐵𝐶 after a dilation with scale factor −2 from the origin.

  • A𝐴′(−8,4), 𝐵′(−10,1), and 𝐶′(−2,1)
  • B𝐴′(−8,8), 𝐵′(−10,2), and 𝐶′(−2,2)
  • C𝐴′(4,−8), 𝐵′(5,−2), and 𝐶′(1,−2)
  • D𝐴′(−8,−8), 𝐵′(−10,−2), and 𝐶′(−2,−2)
  • E𝐴′(8,8), 𝐵′(10,2), and 𝐶′(2,2)

Q6:

The vertices of a quadrilateral 𝐴𝐵𝐶𝐷 are 𝐴(−4,−6), 𝐵(−5,−2), 𝐶, and 𝐷(−6,−9) and the vertices of its image after a dilation with scale factor 𝑋 from the origin are 𝐴′(8,12), 𝐵′, 𝐶′(16,10), and 𝐷(12,18).

Find the scale factor 𝑋.

  • A𝑋=−13
  • B𝑋=−12
  • C𝑋=2
  • D𝑋=−2
  • E𝑋=−3

Find the coordinates of point 𝐶.

  • A𝐶(−48,−30)
  • B𝐶(8,5)
  • C𝐶−163,−103
  • D𝐶(−32,−20)
  • E𝐶(−8,−5)

Find the coordinates of point 𝐵′.

  • A𝐵′(15,6)
  • B𝐵′(10,4)
  • C𝐵′52,1
  • D𝐵′53,23
  • E𝐵′(−10,−4)

Q7:

The vertices of a triangle 𝐴𝐵𝐶 are 𝐴(6,3), 𝐵, and 𝐶(2,2) and the vertices of its image after a dilation with scale factor 𝑋 from the origin are 𝐴′−3,−32, 𝐵′=−32,−3, and 𝐶′.

Find the scale factor 𝑋.

  • A𝑋=−3
  • B𝑋=−2
  • C𝑋=−12
  • D𝑋=12
  • E𝑋=13

Find the coordinates of point 𝐵.

  • A𝐵(−3,−6)
  • B𝐵(3,6)
  • C𝐵34,32
  • D𝐵12,1
  • E𝐵92,9

Find the coordinates of point 𝐶′.

  • A𝐶′(1,1)
  • B𝐶′(−1,−1)
  • C𝐶′(−6,−6)
  • D𝐶′(−4,−4)
  • E𝐶′−23,−23

Q8:

Find the vertices of the image of triangle 𝐴𝐵𝐶 after a dilation with scale factor −2 from the origin.

  • A𝐴(0,2), 𝐵(2,0), 𝐶(4,2)
  • B𝐴(0,−2), 𝐵(−2,0), 𝐶(4,−2)
  • C𝐴(0,−2), 𝐵(2,0), 𝐶(−4,−2)
  • D𝐴(0,2), 𝐵(2,0), 𝐶(−4,−2)
  • E𝐴(0,2), 𝐵(−2,0), 𝐶(−4,2)

Q9:

Find the vertices of the image of triangle 𝐴𝐵𝐶 after a dilation with scale factor −12 centered at the origin.

  • A𝐴′−2,−12, 𝐵′(1,3),𝐶′1,12
  • B𝐴′2,12, 𝐵′(−1,−3), 𝐶′1,12
  • C𝐴′−2,−12, 𝐵′(−1,−3),𝐶′−1,−12
  • D𝐴′(−8,−2), 𝐵′(−4,−12), 𝐶′(−4,−2)
  • E𝐴′−2,−12, 𝐵′(1,3), 𝐶′−1,12

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