# 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 from the origin by a scale factor of 2, and state the coordinates of the image. • A
• B
• C
• D
• E

Q2:

Triangle has been dilated from point to triangle 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: and . Describe the single transformation that would map onto .

• Aa dilation from point 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 by a scale factor of 2
• Ea dilation from point by a scale factor of 2

Hence, determine whether triangles and are similar.

• AThey are similar.
• BThey are not similar.

Q4:

Does a dilation exist that would map triangle to triangle ? 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 from the origin by a scale factor 2, and state the coordinates of the image. • A
• B
• C
• D
• E

Q6:

Dilate the square from the origin by a scale factor of , and state the coordinates of the image. • A
• B
• C
• D
• E

Q7:

The quadrilateral in the given figure has been dilated from the center point to the quadrilateral . What is the scale factor of the dilation? • A2
• B
• C1
• D
• E

Q8:

Find the images of the vertices of the quadrilateral after a dilation with center by a scale factor of . • A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q9:

Triangle is transformed into triangle using a dilation centered on the origin. What is the scale factor? • A
• B
• C
• D
• E3

Q10:

Dilate the rectangle from the origin by a scale factor of , and state the coordinates of the image. • A
• B
• C
• D
• E

Q11:

Dilate triangle from the point (5, 6) by a scale factor of 2, and state the coordinates of the image. • A
• B
• C
• D
• E

Q12:

Dilate triangle from the origin by a scale factor of , and state the coordinates of the image. • A
• B
• C
• D
• E

Q13:

The triangle in the given figure has been dilated from the center point to the triangle . What is the scale factor of the dilation? Q14:

Points , , , and are the vertices of a polygon. List their images after a dilation with scale factor .

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

Q15:

Determine the images of the vertices of after a dilation with a scale factor of 3. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q16:

List the vertices of after a dilation with scale factor . • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q17:

Quadrilateral is transformed to using a dilation. What is the scale factor? • A
• B2
• C
• D
• E

Q18:

has been dilated from the point to the image as seen in the figure. What is the scale factor of the dilation? • A
• B5
• C
• D
• E

Q19:

What is the image of the point with coordinates under a dilation, centered at the origin, with scale factor ?

• A
• B
• C
• D
• E

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?

• Breflection
• Ctranslation
• Drotation

Q22:

Circle is a dilation of circle . What is the scale factor of the dilation? Q23:

Circle is a dilation of circle . What is the scale factor of the dilation? • A
• B
• C
• D
• E

Q24:

Triangle has been dilated from point to triangle and, hence, the two triangles must be similar. What is the scale factor of the dilation?

Q25:

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