Center of Rotation and Circles

If an angle is central in a circle, then the measure of the angle _____ the measure of its intercepted arc.

• is twice

• is half

• is congruent to

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.

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 that maps circle B onto circle A?

• 3/7

• 7/3

• 5/7

• -7/3

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

Does this picture show the diameter or radius of a circle?

• Diameter

• Radius

What is the area of this circle?

• 6082.12

• 1519.76

• 1893.14

• 1292.92

Find the circumference of a circle with a radius of 13.5 mm.

• 37.68mm

• 18.84mm

• 84.78 mm

• none of the above

The following sequence of transformations maps Circle A to Circle B:

• Reflect across the line y = x, then rotate 90^o clockwise

• translate by (x, y) → (x + 6, y - 2) then dilate by scale factor 3/2.

• Translate by (x, y) → (x + 6, y - 2) then dilate by scale factor 2/3.

• Translate by (x, y) → (x - 6, y + 2) then dilate by scale factor 3/2.