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tangare [24]
3 years ago
11

How would you solve this? help.

Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0

Answer:

<em>Center: (3,3)</em>

<em>Radius: </em>2\sqrt{5}<em />

Step-by-step explanation:

<u>Midpoint and Distance Between two Points</u>

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}

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