Question

Which of the following circles lie completely within the fourth quadrant? Check all that apply.

Answer 1

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is where all the points are in the form (positive, negative).

The center and radius of $(x-h)^2+(y-k)^2=r^2$ is (h,k) and r, respectively.

Let's look at the centers and the radius of each of these choices:

A) This one has center (4,-2) and radius $\sqrt{32} \approx 5.7$.

If you add 5.7 to -2 you get a positive number and we needed it negative.

Not this choice; moving on.

B) This one has center (-3,2) and radius $\sqrt{25}=5$.

The center is not even in quadrant 4; moving on.

C) This one has a center (3,-4) and radius 1.

Add 1 to 3 you get 4.

Subtract 1 from 3 you get 2.

Those x's are positive so that looks good so far.

Add 1 to -4 you get -3.

Subtract 1 from -4 you get -5.

Those y's are negative so that looks good.

This circle is in quadrant 4 and doesn't go outside it.

D) This one has center (5,-7) and radius 4.

Add 4 to 5 you get 9.

Subtract 4 from 5 you get 1.

Positive x's is good.

Add 4 to -7 you get -3.

Subtract 4 from -7 you get -11.

Those are negative so that looks good.