Worksheet: Dilation: Positive Scale Factors

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 𝐴𝐵𝐶 from the origin by a scale factor of 2, and state the coordinates of the image.

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

Q2:

Triangle 𝐴𝐵𝐶 has been dilated from point 𝐷 to triangle 𝐴𝐵𝐶 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: 𝐴𝐵𝐶 and 𝐴𝐵𝐶.

Describe the single transformation that would map 𝐴𝐵𝐶 onto 𝐴𝐵𝐶.

  • Aa dilation from point (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 (3,0) by a scale factor of 2
  • Ea dilation from point (2,1) by a scale factor of 2

Hence, determine whether triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

  • AThey are similar.
  • BThey are not similar.

Q4:

Does a dilation exist that would map triangle 𝐴𝐵𝐶 to triangle 𝐹𝐷𝐸? 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 𝐴𝐵𝐶 from the origin by a scale factor 2, and state the coordinates of the image.

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

Q6:

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

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

Q7:

The quadrilateral 𝐴𝐵𝐶𝐷 in the given figure has been dilated from the center point 𝑥 to the quadrilateral 𝐴𝐵𝐶𝐷. What is the scale factor of the dilation?

  • A2
  • B12
  • C1
  • D2
  • E12

Q8:

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

  • A𝐴365,6310, 𝐵365,185, 𝐶92,185, 𝐷92,365
  • B𝐴7710,6710, 𝐵7710,4, 𝐶(5,4), 𝐷5,385
  • C𝐴2710,2710, 𝐵2710,4, 𝐶(5,4), 𝐷5,185
  • D𝐴2310,1310, 𝐵2310,4, 𝐶92,185, 𝐷5,25
  • E𝐴365,6310, 𝐵365,185, 𝐶(5,4), 𝐷92,365

Q9:

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

  • A23
  • B12
  • C13
  • D32
  • E3

Q10:

Dilate the rectangle 𝐴𝐵𝐶𝐷 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)

Q11:

Dilate triangle 𝐴𝐵𝐶 from the point (5, 6) by a scale factor of 2, and state the coordinates of the image.

  • A(2,1),(2,5),(6,3)
  • B(2,3),(5,4),(1,6)
  • C(1,2),(5,2),(3,6)
  • D(4,30),(10,4),(2,6)
  • E(4,6),(10,8),(2,12)

Q12:

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

  • A(4,0),(0,2),(4,2)
  • B(2,0),(0,4),(2,4)
  • C(2,0),(0,2),(2,2)
  • D(0,2),(2,0),(2,2)
  • E(4,0),(0,4),(4,4)

Q13:

The triangle 𝐴𝐵𝐶 in the given figure has been dilated from the center point 𝐷 to the triangle 𝐴𝐵𝐶. What is the scale factor of the dilation?

Q14:

Points (2,1), (5,8), (1,4), and (6,8) are the vertices of a polygon. List their images after a dilation with scale factor 12.

  • A(1,1), 52,8, 12,4, (3,8)
  • B1,12, 52,4, 12,2, (3,4)
  • C(1,1), 52,8, 12,2, (3,4)
  • D32,32, 112,172, 32,72, 112,152
  • E32,32, 112,172, 12,4, (3,8)

Q15:

Determine the images of the vertices of 𝐽𝐾𝐿 after a dilation with a scale factor of 3.

  • A𝐽(3,21), 𝐾(21,12), 𝐿(5,5)
  • B𝐽(3,21), 𝐾(21,12), 𝐿(6,6)
  • C𝐽(4,10), 𝐾(21,12), 𝐿(6,6)
  • D𝐽(21,3), 𝐾(12,21), 𝐿(6,6)
  • E𝐽(4,10), 𝐾(10,7), 𝐿(5,5)

Q16:

List the vertices of 𝐽𝐾𝐿 after a dilation with scale factor 34.

  • A𝐽154,174, 𝐾314,94, 𝐿194,254
  • B𝐽154,174, 𝐾214,94, 𝐿3,214
  • C𝐽154,94, 𝐾94,214, 𝐿214,3
  • D𝐽94,154, 𝐾214,94, 𝐿3,214
  • E𝐽94,154, 𝐾214,94, 𝐿194,254

Q17:

Quadrilateral 𝐿𝑀𝑁𝑃 is transformed to 𝐴𝐵𝐶𝐷 using a dilation. What is the scale factor?

  • A23
  • B2
  • C13
  • D32
  • E12

Q18:

𝐴𝐵 has been dilated from the point 𝐶 to the image 𝐴𝐵 as seen in the figure. What is the scale factor of the dilation?

  • A15
  • B5
  • C16
  • D5
  • E15

Q19:

What is the image of the point with coordinates (𝑥,𝑦) under a dilation, centered at the origin, with scale factor 𝑘?

  • A(𝑥+𝑘,𝑦+𝑘)
  • B𝑥𝑘,𝑦𝑘
  • C(𝑥𝑘,𝑦𝑘)
  • D(𝑥+𝑘,𝑦𝑘)
  • E(𝑥𝑘,𝑦+𝑘)

Q20:

What is the name of the transformation that changes the size of a given figure by a particular scale factor?

  • Areflection
  • Btranslation
  • Chorizontal stretching
  • Ddilation
  • Erotation

Q21:

Consider two circles with different radii. One of the circles can be translated so that they are concentric. Which of the following transformations could be used to transform the radius of one circle to the other?

  • Adilation
  • Breflection
  • Ctranslation
  • Drotation

Q22:

Circle 𝐵 is a dilation of circle 𝐴. What is the scale factor of the dilation?

Q23:

Circle 𝐵 is a dilation of circle 𝐴. What is the scale factor of the dilation?

  • A14
  • B34
  • C12
  • D23
  • E13

Q24:

Triangle 𝐴𝐵𝐶 has been dilated from point 𝐷 to triangle 𝐴𝐵𝐶 and, hence, the two triangles must be similar.

What is the scale factor of the dilation?

Q25:

The image of triangle 𝐴𝐵𝐶 after a dilation from point 𝐷 by a scale factor of four is a triangle 𝐴𝐵𝐶. Which of the following statements is true of triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶?

  • AThe orientations of the two triangles are different.
  • BThe two triangles have equal areas.
  • CThe sides of 𝐴𝐵𝐶 are four times longer than the corresponding sides of triangle 𝐴𝐵𝐶.
  • DThe vertices 𝐴 and 𝐴 are in the same position.
  • EThe two triangles have equal perimeters.

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