# Worksheet: Dilations

In this worksheet, we will practice identifying the scale factor of a dilation of a figure and recognizing when a dilation is part of a combination of transformations.

Q1:

A quadrilateral has been dilated by a scale factor of 2 to . Are and congruent?

• A no
• B yes

Q2:

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

Q3:

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

Q4:

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

Q5:

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

• A
• B
• C
• D
• E

Q6:

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

What is the scale factor of the dilation?

Q7:

Triangle , in the given figure, has been dilated from the point and then reflected to form triangle .

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
• B
• C
• D
• E

Are the triangles similar?

• Ano
• Byes

Q8:

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
• B
• C
• D

Q9:

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

• A The vertices and 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 are four times longer than the corresponding sides of triangle .
• E The two triangles have equal areas.

Q10:

The image after dilating triangle from point , by a scale factor of three, is triangle . Which of the following statements is true of triangles and ?

• AThe vertices and 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.

Q11:

The triangle has been transformed to triangle which has then been transformed to triangle .

Describe the single transformation that maps to .

• Aa reflection in the -axis
• Ba dilation from the origin by a scale factor of 2
• Ca reflection in the -axis
• Da dilation from the origin by a scale factor of 3
• Ea dilation from point by a scale factor of 3

Describe the single transformation that maps to .

• Aa reflection in the -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 -axis
• Ea dilation from the origin by a scale factor of

Hence, are triangles and similar?

• Ano
• Byes

Q12:

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

• A
• B
• C
• D
• E

Q13:

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

Q14:

Triangle can be dilated from point by a scale factor of 2 to the triangle .

Work out the measure of angle .

Work out the measure of angle .

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 are double the measures of the angles in triangle .
• CThey are equal.
• DThe measures of the angles in triangle are half the measures of the angles in triangle .
• EThe measures are tripled.

Q15:

If the points , , and form a triangle, determine the images of its vertices after a dilation with a scale factor of .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q16:

In the given figure, the square has been dilated by a scale factor of two to the square , and the length of is 4.

Work out the perimeter of ?

Work out the area of ?

Q17:

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

• A
• B
• C
• D
• E

Q18:

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

• AOlivia
• BScarlett

Q19:

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

Q20:

Two locations are 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?

• A
• B
• C
• D
• E

Q21:

Given that the scale of the following blueprint for a swimming pool is in. for every 2 ft and that each square has a side length of 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

Q22:

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.

Q23:

Shady is drawing a portrait to a scale of . If the actual dimensions of the portrait are , find the dimensions of the scaled drawing.

• A
• B
• C
• D
• E

Q24:

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

• Athe first model
• Bthe second model

Q25:

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
• B
• C
• D
• E