Question

how would you solve this? help.

Answer 1

Answer:

Center: (3,3)

Radius: $2\sqrt{5}$

Step-by-step explanation:

Midpoint and Distance Between two Points

Given two points A(x1,y1) and B(x2,y2), the midpoint M(xm,ym) between A and B has the following coordinates:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

The distance between both points is given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Point (5,7) is the center of circle A, and point (1,-1) is the center of the circle B. Given both points belong to circle C, the center of C must be the midpoint from A to B:

$\displaystyle x_m=\frac{5+1}{2}=\frac{6}{2}=3$

$\displaystyle y_m=\frac{7-1}{2}=\frac{6}{2}=3$

Center of circle C: (3,3)

The radius of C is half the distance between A and B:

$d=\sqrt{(1-5)^2+(-1-7)^2}$

$d=\sqrt{16+64}=\sqrt{80}=\sqrt{16*5}=4\sqrt{5}$

The radius of C is d/2:

$r =4\sqrt{5}/2 = 2\sqrt{5}$

Center: (3,3)

Radius: $2\sqrt{5}$