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21 votes
Question 4tiple Choice Worth 5 points)

(07.03 MC)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B?
O Translate circle A using the rule (x+4y+3)
O Rotate circle A 45" about the center
O Dilate circle A by a scale factor of 4
O Reflect circle A about the origin

User Anton Poznyakovskiy
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1 Answer

5 votes
5 votes

Answer:

Dilate circle A by a scale factor of 4.

Explanation:

To show that two circles are similar, use transformations to map one to the other.

Step 1

Translate circle A so that its center is the same as circle B.

  • Center of circle A = (6, 7)
  • Center of circle B = (2, 4)

Translate circle A using the rule (x - 4, y - 3)

Step 2

Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.

  • Radius of circle A = 4
  • Radius of circle B = 16

⇒ scale factor = 16 ÷ 4 = 4

Dilate circle A by a scale factor of 4.

Therefore, the only answer option that is correct is:

Dilate circle A by a scale factor of 4.

User Jameen
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2.8k points