Similar Circles

Show that circle C with center (–1, 2) and radius 3 is similar to

circle D with center (3, 4) radius 5.

• Translation: right 4 units, up 2 units; Enlargement ratio: 5/3
• Translation: right 5 units, up 3 units

  Enlargement ratio: 3/5

• Translation: right 4 units, up 2 units Enlargement ratio: 3/5

• Translation: right 2 units, up 4 units

  Enlargement ratio: 5/3

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 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 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.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.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

Circle X is transformed to Circle Y

using a dilation with center (2, 3) and scale factor 4/7 followed by a translation left 3 and down 5.

If the radius of Circle X is 21 units, describe Circle Y.

• Circle Y has a radius of 12 and center (-1, -2).

• Circle Y has a radius of 6 and center (5, 8).

• Circle Y has a radius of 28 and center (-1, -2).

• Circle Y has a radius of 16 and center (5, 8).

Tags

CCSS.HSG.CO.A.2

Show that circle C with center (0, 2) and radius 6 is similar to circle D with center (0, –6) radius 2.

• Circle C is translated up by 8 units to reach circle D, with a scale factor of 2.
• Circle C is translated down by 4 units to reach circle D, with a scale factor of 4.
• Circle C is translated down by 6 units to reach circle D, with a scale factor of 1.5.
• Circle C is translated down by 8 units to reach circle D, with a scale factor of 3.

Tags

CCSS.7.G.A.1

Show the two given circles are similar by stating the necessary transformations from C to D.

C: center (2, 3) radius 5;

D: center (–1, 4) radius 10.

• Circles C and D are similar by translating C to (-1, 4) and dilating by a factor of 2.
• Translating C to (-1, 3) and dilating by a factor of 4.
• Translating C to (0, 3) and dilating by a factor of 1.5.
• Translating C to (2, 4) and dilating by a factor of 3.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Show the two given circles are similar by stating the necessary transformations from C to D.

C: center (0, –3) radius 2;

D: center (–2, 5) radius 6

• Circles C and D are similar by translating C to D and scaling the radius by a factor of 3.
• Circles C and D are similar by translating C to D without any scaling.
• Circles C and D are similar by reflecting C to D and scaling the radius by a factor of 4.
• Circles C and D are similar by rotating C to D and scaling the radius by a factor of 2.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Show the two given circles are similar by stating the necessary transformations from C to D

C: center (–2, 8) radius 4;

D: center (0, 4) radius 9

• Translate left 2 units and up 4 units, then dilate by a scale factor of 4/9.
• Translate right 4 units and down 2 units, then dilate by a scale factor of 3/2.
• Translate left 4 units and up 2 units, then dilate by a scale factor of 2/3.
• Translate right 2 units and down 4 units, then dilate by a scale factor of 9/4.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2