geometry practice ?n's?

Question

1. What are the coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5)?


A.
(5, 1)

B.
(3, 3)

C.
(2.5, 2.5)

D.
(0, 0)

2.The circle x2 + y2 = 36 is translated 5 units left and 4 units up. Where is the center of the new circle after the translation?
A.
(-5,-4)

B.
(5,-4)

C.
(-5, 4)

D.
(5, 4)

3. Which equation represents the image of circle (x 5)2 + (y + 12)2 = 169 after a translation 2 units right and 3 units down?
A.
(x - 7)2 + (y + 15)2 = 169

B.
(x - 3)2 + (y + 9)2 = 169

C.
(x+ 7)2 + (y - 15)2 = 169

D.
(x+ 3)2 + (y - 9)2 = 169

4.Describe the translation of circle (x - 1)2 + (y - 4)2 = 25 that results in an image whose equation is (x + 1)2 + (y - 5)2 = 25.
A.
Two units right and one unit down.

B.
Two units right and one unit up.

C.
Two units left and one unit down.

D.
Two units left and one unit up.

these are practice prob. so please help!

can someone help please!?

Answer 1

For the first one, remember that the perpendicular bisectors of any 2 chords of a circle intersect at the origin. For the rest, the general equation for a circle is
(x - a)^2 + (y - b)^2 = r^2,
where the center lies at point (a,b).

Answer 2

a quick solution to the first is to realize that the points create a right triangle. The right angle is inscribed in a semicircle, so the center of the circle is the midpoint of the hypotenuse -- find the midpoint of (1,1) and (5,5) and it is (3,3).

Translating circles from the origin results in equations of the form:

(x-h)^2 + (y-k)^2 = r^2 with horizontal translation h and vertical translation k.