Question

Given circle A, centered at A(7, 1) with a radius of 8 cm and Circle B, centered at B(-1, 3) with a diameter of 16cm, determine which of the following transformations would establish that they are similar circles.

A. Dilate Circle A about A by a scale factor of 2 followed by a translation of 8 left and 2 up.


B. Translate Circle A 8 left and 2 up.


C. Dilate Circle B about B by a scale factor of 1/2 followed by a translation of 8 left and 2 up.


D. Dilate Circle B about B by a scale factor of 1/2 followed by a translation of 8 right and 2 down.

Answer 1

Translate Circle A 8 left and 2 up answer (B)

Explanation:

Circle A has radius 8 cm and center (7 , 1)

Circle B has radius 16/2 = 8 cm and center (-1 , 3)

∵ There is no change in the radius because 2 circles have equal radii

∴It is translation (translation does not change the dimensions of the figure)

∵ A moved horizontally from 7 to -1

∴ It Moved to the left by (7 - -1 = 8) 8

∵ A moved vertically from 1 to 3

∴ It moved up by (3 - 1 = 2) 2