Question

Which sequences of transformations will map circle

M onto circle N?

Answer 1

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Explanation:

Given

See attachment for M and N

Required

Which maps M to N

The coordinates of the radius of the circles are:

`M = (5,5)`

`N = (5,-5)`

And the radius of circles are:

`r_M=2`

`r_N=3`

The first transformation from M to M' is:

- Reflect across the x-axis

The rule is:

`(x,y) \to (x,-y)`

`M(5,5) \to M'(5,-5)`

At this point, M' and N now have the same center but different radius.

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

`k =(r_N)/(r_M)`

`k =(3)/(2)`

At this point, M has been completely mapped to N.