Open the “Circle: the role of the radius” applet. Place the cursor on point B, press and hold the mouse button. Drag B around the Cartesian plane.

(a) What is the center of the circle?

(b) Move B to a point in the Cartesian plane directly above the center such that the radius of the circle is 5.

(c) Move B to a point in the Cartesian plane such that the radius of the circle is 4.

(d) Move B to a point in the Cartesian plane such that the radius of the circle is 3.

(e) Find the coordinates of two points with integer coordinates in the fourth quadrant on the circle that result in a circle of radius 5 with center equal to that found in part (a).

(f) Use the concept of symmetry about the center, vertical line through the center of the circle, and horizontal line through the center of the circle to find three other points with integer coordinates in the other three quadrants that lie on the circle of radius five with center equal to that found in part (a).