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This printable supports Common Core Mathematics Standard HSG-SRT.A.1, HSG-SRT.A.1b

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Dilation and Length (Grade 9)

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Dilation and Length

1. 
Line segment [math]bar{AB}[/math] is dilated by a factor of 3 with the origin as the center of dilation. What is the length of the dilated line segment, [math]A'B'[/math], in relation to [math]AB ?[/math]
  1. [math]A'B' = AB + 3[/math]
  2. [math]A'B' = 3AB[/math]
  3. [math]A'B' = 1/3 AB[/math]
  4. [math]A'B' = AB[/math]
2. 
Line segment [math]bar{MN}[/math] is dilated by a factor of 1/5, with the center of dilation being the origin. What is the length of the dilated line segment, [math]M'N'[/math], in relation to [math]MN ?[/math]
  1. [math]M'N' = 5MN[/math]
  2. [math]M'N' = 1/5 + MN[/math]
  3. [math]M'N' = 1/5 MN[/math]
  4. [math]M'N' = (1/5)^2 MN[/math]
3. 
Line segment [math]bar{PQ}[/math] is dilated by a factor of 2/3, with the center of dilation being (-3,-2). Determine the length of the dilated line segment, [math]P'Q'[/math], in relation to [math]PQ[/math].
  1. [math]P'Q' = 2/3 PQ[/math]
  2. [math]P'Q' = 3/2 PQ[/math]
  3. [math]P'Q' = 9/4 PQ[/math]
  4. Not enough information given.
4. 
Line segment [math]bar{GH}[/math] is dilated by a factor of -5/2, with the center of dilation being (-7,-9). Determine the length of the dilated line segment, [math]G'H'[/math], in relation to [math]GH[/math].
  1. [math]G'H' = 25/4 GH[/math]
  2. [math]G'H' = -2/5 GH[/math]
  3. [math]G'H' = 5/2GH[/math]
  4. Not enough information given.
5. 
Line segment [math]bar{AB}[/math] has endpoints [math]A(1,2)[/math] and [math]B(9,6)[/math]. If [math]bar{AB}[/math] undergoes a dilation of factor of 3 centered at the origin, what is the length of the dilated line segment? Round the answer to one decimal place, if necessary.
  1. 26.8 units
  2. 8.9 units
  3. 3.0 units
  4. 6 units
6. 
Line segment [math]bar{PQ}[/math] has endpoints [math]P(3,4)[/math] and [math]Q(6,2)[/math]. If [math]bar{PQ}[/math] undergoes a dilation of factor 1/2 centered at the origin, what is the length of the dilated line segment? Round the answer to one decimal place, if necessary.
  1. 7.2 units
  2. 3.6 units
  3. 1.8 units
  4. 3 units
7. 
Line segment [math]bar{ST}[/math] has endpoints [math]S(-3,4)[/math] and [math]T(1,-1)[/math]. If [math]bar{ST}[/math] undergoes a dilation of factor -3/4, centered at the origin, what is the length of the dilated line segment? Round the answer to one decimal place.
  1. 2.4 units
  2. 8.5 units
  3. 6.4 units
  4. 4.8 units
8. 
Line segment [math]bar{AB}[/math] has endpoints [math]A(9,4)[/math] and [math]B(-1,8)[/math]. If [math]bar{AB}[/math] is dilated by a factor of -5, with [math](6,7)[/math] being the center of dilation, what is the length of the dilated line segment? Round the answer to one decimal place.
  1. 53.9 units
  2. 16.1 units
  3. 10.8 units
  4. 2.2 units
9. 
[math]Delta ABC[/math] is dilated by a factor of 2 with the origin as the center of dilation. Which of the following gives the perimeter of the image [math]Delta A'B'C' ?[/math]
  1. [math]2 AB + BC + AC[/math]
  2. [math]2AB + 2BC + 2AC[/math]
  3. [math]2^3(AB+ BC+AC)[/math]
  4. [math]2A'B' + 2B'C' + 2A'C'[/math]
10. 
Square ABCD has an area of 4 square units. If ABCD is dilated by a factor of 3 with the center of dilation being the origin, what is the area of the dilated square?
  1. 7 square units
  2. 12 square units
  3. 16 square units
  4. 36 square units

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