Similar Circles

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

• Dilate circle I 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 with scale factor 1/2 and then translate left 4 and down 6.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

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

• Translate circle A left 7, up 6 and then dilate with scale factor 2/5 .

• Dilate circle A at 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.HSG.SRT.A.2

CCSS.8.G.A.4

Circle B is the pre-image and Circle A is the image. Which transformations map Circle B onto Circle A?

• (x, y)→(x − 4, y + 8); dilation by scale factor of 3/4 at center of circle

• (x, y)→(x + 4, y − 8); dilation by scale factor of 4/3 at center of circle

• (x, y)→(x − 4, y + 8); dilation by scale factor of 4/3 at center of circle

• (x, y)→(x − 4, y + 8); dilation by scale factor of 1/2 at center of circle

Tags

CCSS.HSG.SRT.A.2

CCSS.8.G.A.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.HSG.SRT.A.2

CCSS.8.G.A.4

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 12 while Circle Y has a radius of 6.

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

Tags

CCSS.7.G.A.1

The best way to demonstrate that all circles are similar is to show that

• they're all round

• they all have centers

• a combination of transformations can 'make' one circle become another

• since pi is 3.14, and pies are round and circular, then it's obvious

Tags

CCSS.8.G.A.3

Proving which pair of circles to be similar would involve a scale factor of 2 and a translation of 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

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Circle B is mapped to Circle D using a dilation with center (1, -7) and scale factor 3/5 followed by a translation right 2 and up 6. If the radius of Circle B is 15 units, describe Circle D.

• Circle D has a radius of 9 and center (3, -1).

• Circle D has a radius of 3 and center (-1, -13).

• Circle D has a radius of 25 and center (3, -1).

• Circle D has a radius of 12 and center (-1, -13).

Tags

CCSS.HSG.CO.A.2

What are the coordinates of the center and the radius of the circle with equation (x - 4)² + (y - 3)² = 25 ?

• Center (4, 3)

  Radius = 5 units

• Center (4, 3)

  Radius = 25 units

• Center (-4, -3)

  Radius = 25 units

• Center (-4, -3)

  Radius = 5 units

Tags

CCSS.HSG.GPE.A.1

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

Tags

CCSS.HSG.GPE.A.1