7.1 Circle Similarity

What is the translation vector for Circle B to Circle A?

• (x, y) →(x + 8, y - 4)

• (x, y) →(x - 4, y +8 )

• (x, y) →(x - 8, y + 4)

• (x, y) →(x + 4, y - 8)

What is the dilation scale factor for mapping circle B onto circle A?

• 9/16

• 4/3

• 3/4

• 1

What is the translation mapping rule that maps Circle B onto Circle A?

• (x, y) → (x - 4, y + 1)

• (x, y) → (x + 1, y - 4)

• (x, y) → (x - 1, y + 4)

• (x, y) → (x + 4, y - 1)

What is the dilation scale factor that maps circle B onto circle A?

• 3/7

• 7/3

• 5/7

• -7/3

Jake says “Two circles are always similar no matter what because you can map one onto the other using similarity transformations!!”  What transformations might he be referring to?

• Rotation & Translation
• Translation & Dilation
• Reflection & Dilation
• Dilation & Rotation

Two circles A and B have different radii.  A student dilates circle A at its center by a scale factor of 9/4 to make it the same size as circle B.  What scale factor could have been used to make circle B the same size as circle A?

• 3/2
• 2/3
• 4/9
• 9/4

Circle A has center (2, 7) and radius 2. Circle B has center (9, 1) and radius 5. Which transformations can be used to show that the two circles are similar?

• Translate circle A right 7 and down 6 and then dilate with scale factor 5/2 and center (9, 1)

• Translate circle A left 7, up 6 and then dilate with scale factor 2/5 and center (9, 1).

• Dilate circle A using center (2, 7) and scale factor 2/5 then translate right 7 and down 6

• Reflect circle A over x = 5.5 and translate up 6 units.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

What transformations can be used to show circles I and J are similar?

• Dilate circle I about (4, 10) with scale factor 1/2 and then translate down 4 and left 6.

• Translate circle J right 4 and up 6 and then dilate about point (4, 10) with a scale factor 1/2

• Translate circle J left 6 and down 4 and then dilate about point (4, 10) with scale factor 2.

• Dilate circle I about (4, 10) with scale factor 1/2 and then translate left 4 and down 6.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Circles X and Y have a similarity ratio of 1/2. Which of the following could NOT be true about the circles?

• Circle X has a radius of 5 while Circle Y has a radius of 10.

• Circle X has a circumference of 15π and Circle Y has a circumference of 30π.

• Circle X has a radius of 6 while Circle Y has a radius of 12.

• Circle X has a circumference of 60π while Circle Y has a circumference of 20π.

Which pair of circles could be proven similar by dilating by a scale factor of 2 and translating right 10 and down 2?

• Circle L to Circle M

• Circle K to Circle L

• Circle K to Circle M

• Circle N to Circle L