Lesson Worksheet: Dilation: Negative Scale Factors Mathematics

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 𝐴𝐵𝐶 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
  • B12
  • C4
  • D12
  • E2

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)
  • C𝐶163,103
  • D𝐶(32,20)
  • E𝐶(8,5)

Find the coordinates of point 𝐵.

  • A𝐵(15,6)
  • B𝐵(10,4)
  • C𝐵52,1
  • D𝐵53,23
  • 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 𝐴3,32, 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)
  • E𝐶23,23

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.

  • A𝐴2,12, 𝐵(1,3),𝐶1,12
  • B𝐴2,12, 𝐵(1,3), 𝐶1,12
  • C𝐴2,12, 𝐵(1,3),𝐶1,12
  • D𝐴(8,2), 𝐵(4,12), 𝐶(4,2)
  • E𝐴2,12, 𝐵(1,3), 𝐶1,12

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