Question

Which transformations can be used to show that circle m is similar to circle n? circle m: center (−1, 10) and radius 3 circle n: center (0, 10) and radius 15 select each correct answer. circle n is a dilation of circle m with a scale factor of 5. circle m and circle n are congruent. circle n is a translation of circle m, 1 unit right. circle m is a dilation of circle n with a scale factor of 12?

Answer 1

Answer: Both starting with Circle N

Explanation:

1 unit right and scale factor of 5

Answer 2

The correct statements that is used to show that circle m is similar to circle n is:

• circle n is a dilation of circle m with a scale factor of 5.
• circle n is a translation of circle m, 1 unit right.

Explanation:

We know that two circles are said to be similar if by using some translation and some dilation it could be mapped to the other.

Circle m is given as:

circle m: center (−1, 10) and radius 3

That means the equation of circle m is:

`(x+1)^2+(y-10)^2=3^2`

Circle n is given as:

circle n: center (0, 10) and radius 15

That means that the equation of circle n is:

`(x)^2+(y-10)^2=15^2`

1)

circle n is a dilation of circle m with a scale factor of 5.

This option is correct.

Since, the radius of circle n is 5 times the radius of circle m.

2)

circle m and circle n are congruent.

This option is incorrect.

Since, the radius of both the circles are unequal and hence they can't be congruent.

3)

circle n is a translation of circle m, 1 unit right.

This option is correct.

Since, the center of circle m is: (-1,10)

and center of circle n is: (0,10)

That means m is to be shifted one unit to the right.

4)

circle m is a dilation of circle n with a scale factor of 12.

This option is incorrect.

Since circle m is a circle with smaller radius hence it can't be a dilation of circle n with scale factor greater than one.