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.

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.

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 right 2 units and down 4 units, then dilate by a scale factor of 9/4.

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.

Transform circle F to circle F' by translating it and then performing a dilation. Find the translation rule and the scale factor of the dilation.

Translation rule: (x, y) -> (x - 10, y + 9); Scale factor: 1.5

Translation rule: (x, y) -> (x + 10, y); Scale factor: 0.5

Translation rule: (x, y) -> (x + 5, y + 5); Scale factor: 3

Translation rule: (x, y) -> (x - 8, y - 8); Scale factor: 1

Circle F to circle F' by translating it and then performing a dilation. Find the translation rule and the scale factor of the dilation.

Translation rule: (x, y) -> (x -11, y - 10); Scale factor: 0.67

Translation rule: (x, y) -> (x - 4, y + 1); Scale factor: 5

Translation rule: (x, y) -> (x -11, y - 10); Scale factor: 1.5

Translation rule: (x, y) -> (x - 2, y + 6); Scale factor: 2

You can transform circle F to circle F' by translating it and then performing a dilation. Circle F (6, -6) and Circle F’ (3, 2) and the radius F is 3 and the radius of F’ is 5. Find the translation rule and the scale factor of the dilation.

Translation rule: (x, y) -> (x - 3, y + 8); Scale factor: 5/3

Translation rule: (x, y) -> (x + 3, y - 8); Scale factor: 3/5

Translation rule: (x, y) -> (x - 5, y + 2); Scale factor: 2

Translation rule: (x, y) -> (x + 1, y + 1); Scale factor: 1

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?

Yes, it can be translated and then dilated.

It can only be rotated and reflected.

It can be stretched but not translated.

It can only be translated without dilation.

Circle A and circle B are concentric. What does that mean?

Circle A and circle B are concentric means they have the same center.

Circle A and circle B are the same size.

Circle A is larger than circle B.

Circle A and circle B are tangent to each other.

To prove Similarity between Circle A center at A (-2,5) with radius of 5 cm. Circle B at (5,-3) with a radius of 15 cm. Janice translates circle A by vector <7,-8> and dilates circle A at point B by a scale factor of 3. Provide transformation sequences to establish Similarity ?

1. Translate circle B by vector . 2. Dilate circle B at the new center by a scale factor of 1/3.

Dilate circle B at the new center by a scale factor of 2.

Translate circle B by vector and dilate by a scale factor of 4.

Similar Circles

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

8.G.A.4, HSG.CO.A.2, 8.G.A.2

Standards-aligned

HANNA GRUBB

Used 3+ times

FREE Resource

24 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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Similar Circles

24 questions

Show that circle C with center (–1, 2) and radius 3 is similar to circle D with center (3, 4) radius 5.

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

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

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?

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 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.

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

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.

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

Show the two given circles are similar by stating the necessary transformations from C to DC: center (–2, 8) radius 4; D: center (0, 4) radius 9

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Discover more resources for Mathematics

Show that circle C with center (–1, 2) and radius 3 is similar to
circle D with center (3, 4) radius 5.

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

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.

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.

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

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