Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: Dilations

Q1:

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

  • Arotation
  • Btranslation
  • Creflection
  • Ddilation
  • Ehorizontal stretching

Q2:

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?

  • A reflection
  • B rotation
  • C translation
  • D dilation

Q3:

In the given figure, what is the scale factor between circle 𝐴 and circle 𝐡 ?

  • A3
  • B1
  • C 1 2
  • D2
  • E 1 3

Q4:

In the given figure, what is the scale factor between circle 𝐴 and circle 𝐡 ?

  • A 1 3
  • B 1 4
  • C 3 4
  • D 2 3
  • E 1 2

Q5:

Triangle 𝐴 𝐡 𝐢 has been dilated from point 𝐷 to triangle 𝐴 𝐡 𝐢 β€² β€² β€² and, hence, the two triangles must be similar.

What is the scale factor of the dilation?

Q6:

Triangle 𝐴 𝐡 𝐢 , in the given figure, has been dilated from the point 𝐺 and then reflected to form triangle 𝐷 𝐸 𝐹 .

State the scale factor of the enlargement.

  • Ascale factor = 3
  • Bscale factor = 1
  • Cscale factor = 4
  • Dscale factor = 2
  • Escale factor = 5

State the line of reflection.

  • A 𝑦 = βˆ’ π‘₯ + 2
  • B 𝑦 = βˆ’ 2 π‘₯ + 2
  • C 𝑦 = π‘₯ βˆ’ 2
  • D 𝑦 = π‘₯ + 2
  • E 𝑦 = 2 π‘₯ + 2

Are the triangles similar?

  • Ano
  • Byes

Q7:

The perimeter of a piece of land in the shape of an equilateral triangle is 720 m. When a scale drawing is made, the length of side of the triangle is 2 cm. What is the drawing scale?

  • A 1 3 6 0 0 0 :
  • B 1 1 2 0 0 0 0 :
  • C 1 3 6 0 0 0 0 :
  • D 1 1 2 0 0 0 :

Q8:

The image of triangle 𝐴 𝐡 𝐢 after a dilation from point 𝐷 by a scale factor of four is a triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² . Which of the following statements is true of triangles 𝐴 𝐡 𝐢 and 𝐴 β€² 𝐡 β€² 𝐢 β€² ?

  • A The vertices 𝐴 and 𝐴 β€² are in the same position.
  • B The two triangles have equal perimeters.
  • C The orientations of the two triangles are different.
  • D The sides of 𝐴 β€² 𝐡 β€² 𝐢 β€² are four times longer than the corresponding sides of triangle 𝐴 𝐡 𝐢 .
  • E The two triangles have equal areas.

Q9:

The image after dilating triangle 𝐴 𝐡 𝐢 from point 𝐷 , by a scale factor of three, is triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² . Which of the following statements is true of triangles 𝐴 𝐡 𝐢 and 𝐴 β€² 𝐡 β€² 𝐢 β€² ?

  • AThe vertices 𝐴 and 𝐴 β€² are in the same position.
  • BThe two triangles have equal perimeters.
  • CThe orientations of the two triangles are different.
  • DThe angles in the two triangles are equal.
  • EThe two triangles have equal areas.

Q10:

The triangle 𝐴 𝐡 𝐢 has been transformed to triangle 𝐴 𝐡 𝐢 β€² β€² β€² which has then been transformed to triangle 𝐴 𝐡 𝐢 β€² β€² β€² β€² β€² β€² .

Describe the single transformation that maps 𝐴 𝐡 𝐢 to 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa reflection in the π‘₯ -axis
  • Ba dilation from the origin by a scale factor of 2
  • Ca reflection in the 𝑦 -axis
  • Da dilation from the origin by a scale factor of 3
  • Ea dilation from point ( 0 , 1 ) by a scale factor of 3

Describe the single transformation that maps 𝐴 β€² 𝐡 β€² 𝐢 β€² to 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa reflection in the π‘₯ -axis
  • Ba dilation from the origin by a scale factor of 2
  • Ca dilation from the origin by a scale factor of 3
  • Da reflection in the 𝑦 -axis
  • Ea dilation from the origin by a scale factor of 1 3

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² similar?

  • Ano
  • Byes

Q11:

Dilate triangle 𝐴 𝐡 𝐢 from the origin by a scale factor of βˆ’ 2 , and state the coordinates of the image.

  • A ( βˆ’ 4 , 0 ) , ( 0 , βˆ’ 8 ) , ( βˆ’ 4 , βˆ’ 8 )
  • B ( βˆ’ 4 , 0 ) , ( 0 , 4 ) , ( βˆ’ 4 , 4 )
  • C ( 8 , 0 ) , ( 0 , 4 ) , ( 8 , 4 )
  • D ( 8 , 0 ) , ( 0 , βˆ’ 8 ) , ( 8 , βˆ’ 8 )
  • E ( 0 , 8 ) , ( βˆ’ 8 , 0 ) , ( βˆ’ 8 , 8 )

Q12:

A triangle with a perimeter of 16 has been dilated by a scale factor of 1 2 . What is the perimeter of the image?

Q13:

Triangle 𝐷 𝐸 𝐹 can be dilated from point 𝐺 by a scale factor of 2 to the triangle 𝐴 𝐡 𝐢 .

Work out the measure of angle 𝐴 𝐢 𝐡 .

Work out the measure of angle 𝐷 𝐸 𝐹 .

What is true of the measures of the angles in both triangles?

  • AThe measures of the angles in both triangles depend on their lengths.
  • BThe measures of the angles in triangle 𝐷 𝐸 𝐹 are double the measures of the angles in triangle 𝐴 𝐡 𝐢 .
  • CThey are equal.
  • DThe measures of the angles in triangle 𝐷 𝐸 𝐹 are half the measures of the angles in triangle 𝐴 𝐡 𝐢 .
  • EThe measures are tripled.

Q14:

If the points 𝐽 ( 4 , 6 ) , 𝐾 ( 8 , 7 ) , and 𝐿 ( 8 , 2 ) form a triangle, determine the images of its vertices after a dilation with a scale factor of 2 3 .

  • A 𝐽 β€² ο€Ό 8 3 , 6  , 𝐾 β€² ο€Ό 1 6 3 , 7  , 𝐿 β€² ο€Ό 1 6 3 , 2 
  • B 𝐽 β€² ο€Ό 1 4 3 , 2 0 3  , 𝐾 β€² ο€Ό 1 6 3 , 1 4 3  , 𝐿 β€² ο€Ό 1 6 3 , 4 3 
  • C 𝐽 β€² ο€Ό 8 3 , 4  , 𝐾 β€² ο€Ό 1 6 3 , 1 4 3  , 𝐿 β€² ο€Ό 2 6 3 , 8 3 
  • D 𝐽 β€² ο€Ό 8 3 , 4  , 𝐾 β€² ο€Ό 1 6 3 , 1 4 3  , 𝐿 β€² ο€Ό 1 6 3 , 4 3 
  • E 𝐽 β€² ο€Ό 1 4 3 , 2 0 3  , 𝐾 β€² ο€Ό 2 6 3 , 2 3 3  , 𝐿 β€² ο€Ό 2 6 3 , 8 3 

Q15:

In the given figure, the square 𝐴 𝐡 𝐢 𝐷 has been dilated by a scale factor of two to the square 𝐴 𝐡 𝐢 𝐷 β€² β€² β€² β€² , and the length of 𝐴 𝐡 is 4.

Work out the perimeter of 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² ?

Work out the area of 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² ?

Q16:

An architect made a model for a building that is to be 154 meters tall. Given that the model is 27.5 centimeters tall, determine the scale of the model.

  • A 1 = 5 6 0 c m m
  • B 1 = 0 . 2 c m m
  • C 1 = 1 2 6 . 5 c m m
  • D 1 = 5 . 6 c m m
  • E 1 = 1 5 4 c m m

Q17:

On a certain map, 1 inch represents 7 feet. Scarlett believes the scale factor of the map to be 1 7 : , and Olivia believes it to be 1 8 4 : . Who is correct?

  • AOlivia
  • BScarlett

Q18:

A graphic designer wants to enlarge a design by a scale factor of 4.5. Given that the original design was 48 inches wide and 27 inches long, determine the dimensions of the enlarged version.

  • A 52 inches wide and 32 inches long
  • B 10.7 inches wide and 6 inches long
  • C 49 inches wide and 28 inches long
  • D 216 inches wide and 121.5 inches long
  • E 47 inches wide and 26 inches long

Q19:

Two locations are 6 3 4 inches apart on a map. If the actual distance between the two locations is 278 miles, which of the following is the map’s scale?

  • A3 inches = 1 1 1 2 miles
  • B1 inch = 2 7 8 miles
  • C3 inches = 1 3 9 miles
  • D27 inches = 1 1 1 2 miles
  • E27 inches = 1 3 9 miles

Q20:

Given that the scale of the following blueprint for a swimming pool is 1 4 in. for every 2 ft and that each square has a side length of 1 4 in, what are the actual dimensions of the pool?

  • A 4 ft wide, 7 ft long
  • B 6 ft wide, 12 ft long
  • C 8 ft wide, 14 ft long

Q21:

If you dilate a line by a given scale factor from a point not on the line, which property would be true of the line and its image?

  • A The lines would be skew.
  • B The lines would be perpendicular.
  • C The lines would be coincident.
  • D The lines would be parallel.
  • E The lines would be intersecting.

Q22:

Anthony is drawing a portrait to a scale of 1 ∢ 5 . If the actual dimensions of the portrait are 6 0 Γ— 9 0 c m c m , find the dimensions of the scaled drawing.

  • A 6 Γ— 9 c m c m
  • B 2 Γ— 3 c m c m
  • C 3 0 Γ— 4 5 c m c m
  • D 1 2 Γ— 1 8 c m c m
  • E 3 0 0 Γ— 4 5 0 c m c m

Q23:

Two models are built for the same object. The first model is built on a 1 4 0 : scale, and the second model is built on a 1 5 1 : scale. Which is the larger model?

  • Athe first model
  • Bthe second model

Q24:

An architect made a 5-feet-tall scale model of a building. Given that the actual height of the building is 57 feet6 inches, how many times as tall as the actual building is the model?

  • A 5 6 3
  • B 2 3 2
  • C 6 3 5
  • D 2 2 3
  • E 5 5 7

Q25:

James wants to scale a photograph of his family by a factor of 9 4 . Given that the original image is 6 inches wide and 3 inches high, determine the dimensions of the scaled image.

  • A 13.5 inches wide and 5.25 inches high
  • B 8.25 inches wide and 5.25 inches high
  • C 2.67 inches wide and 6.75 inches high
  • D 13.5 inches wide and 6.75 inches high
  • E 2.67 inches wide and 1.33 inches high