Lesson Worksheet: Dilation: Positive Scale Factors Mathematics • 8th Grade

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

Q1:

Dilate triangle 𝐴𝐡𝐢 from the origin by a scale factor of 2, and state the coordinates of the image.

  • A(0,4),(2,1),(βˆ’3,1)
  • B(0,βˆ’4),(4,2),(βˆ’6,2)
  • C(βˆ’4,0),(2,2),(2,βˆ’3)
  • D(βˆ’2,0),(1,2),(1,βˆ’3)
  • E(βˆ’4,0),(2,4),(2,βˆ’6)

Q2:

Triangle 𝐴𝐡𝐢 has been dilated from point 𝐷 to triangle 𝐴𝐡𝐢 and, hence, the two triangles must be similar. What do you notice about the measures of the angles in both shapes?

  • AThe measures tripled.
  • BThe measures doubled.
  • CThe measures were divided by three.
  • DThe measures were halved.
  • EThey are equal.

Q3:

The figure shows two triangles: 𝐴𝐡𝐢 and 𝐴𝐡𝐢.

Describe the single transformation that would map 𝐴𝐡𝐢 onto 𝐴′𝐡′𝐢′.

  • Aa dilation from point (βˆ’1,2) by a scale factor of 2
  • Ba translation of one up and one right
  • Ca translation of one up and two right
  • Da dilation from point (βˆ’3,0) by a scale factor of 2
  • Ea dilation from point (βˆ’2,1) by a scale factor of 2

Hence, determine whether triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′ are similar.

  • AThey are similar.
  • BThey are not similar.

Q4:

Does a dilation that would map triangle 𝐴𝐡𝐢 to triangle 𝐹𝐷𝐸 exist? If yes, state the scale factor.

  • AYes, a dilation by a scale factor of 2
  • BYes, a dilation by a scale factor of 6
  • CNo dilation exists.
  • DYes, a dilation by a scale factor of 3
  • EYes, a dilation by a scale factor of 4

Q5:

Dilate triangle 𝐴𝐡𝐢 from the origin by a scale factor 2, and state the coordinates of the image.

  • A(4,βˆ’10),(8,βˆ’6),(0,βˆ’4)
  • B(βˆ’5,2),(βˆ’3,4),(βˆ’2,0)
  • C(βˆ’10,βˆ’4),(βˆ’6,βˆ’8),(βˆ’4,0)
  • D(2,βˆ’5),(4,βˆ’3),(0,βˆ’2)
  • E(βˆ’10,4),(βˆ’6,8),(βˆ’4,0)

Q6:

Dilate the square 𝐴𝐡𝐢𝐷 from the origin by a scale factor of 12, and state the coordinates of the image.

  • A(βˆ’3,1),(βˆ’5,1),(βˆ’5,3),(βˆ’3,3)
  • B(βˆ’6,1),(βˆ’10,1),(βˆ’10,3),(βˆ’6,3)
  • C(1,βˆ’3),(1,βˆ’5),(3,βˆ’5),(βˆ’3,3)
  • D(βˆ’6,2),(βˆ’10,2),(βˆ’10,6),(βˆ’6,6)
  • E(βˆ’3,2),(βˆ’5,2),(βˆ’5,6),(βˆ’3,6)

Q7:

The quadrilateral 𝐴𝐡𝐢𝐷 in the given figure has been dilated from the center point π‘₯ to the quadrilateral 𝐴′𝐡′𝐢′𝐷′. What is the scale factor of the dilation?

  • A2
  • Bβˆ’12
  • C1
  • Dβˆ’2
  • E12

Q8:

Find the images of the vertices of the quadrilateral 𝐴𝐡𝐢𝐷 after a dilation with center 𝐢 by a scale factor of 910.

  • Aπ΄β€²ο€Όβˆ’365,βˆ’6310, π΅β€²ο€Όβˆ’365,βˆ’185, πΆβ€²ο€Όβˆ’92,βˆ’185, π·β€²ο€Όβˆ’92,βˆ’365
  • Bπ΄β€²ο€Όβˆ’7710,βˆ’6710, π΅β€²ο€Όβˆ’7710,βˆ’4, 𝐢′(βˆ’5,βˆ’4), π·β€²ο€Όβˆ’5,βˆ’385
  • C𝐴′2710,2710, 𝐡′2710,βˆ’4, 𝐢′(βˆ’5,βˆ’4), π·β€²ο€Όβˆ’5,185
  • Dπ΄β€²ο€Όβˆ’2310,βˆ’1310, π΅β€²ο€Όβˆ’2310,βˆ’4, πΆβ€²ο€Όβˆ’92,βˆ’185, π·β€²ο€Όβˆ’5,βˆ’25
  • Eπ΄β€²ο€Όβˆ’365,βˆ’6310, π΅β€²ο€Όβˆ’365,βˆ’185, 𝐢′(βˆ’5,βˆ’4), π·β€²ο€Όβˆ’92,βˆ’365

Q9:

Triangle 𝐿𝑀𝑁 is transformed into triangle 𝐴𝐡𝐢 using a dilation centered on the origin. What is the scale factor?

  • A23
  • B12
  • C13
  • D32
  • E3

Q10:

Dilate the rectangle 𝐴𝐡𝐢𝐷 from the origin by a scale factor of 13, and state the coordinates of the image.

  • A(6,1),(3,1),(3,3),(6,3)
  • B(6,3),(3,3),(3,9),(6,9)
  • C(3,3),(1,3),(1,9),(2,9)
  • D(2,1),(1,1),(1,3),(2,3)
  • E(1,2),(1,1),(3,1),(3,2)

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