Question

Which sequences of transformations will map circle M onto circle N?

Answer 1

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step 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.

$k =\frac{r_N}{r_M}$

$k =\frac{3}{2}$

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