MATHEMATICS HIGH SCHOOL

Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?C(-1, -2)

D(-6, 3)

E(-3, -3)

F(-2, 6)

Answers

Answer 1
Answer: The equation of a circle:
(x-h)^2+(y-k)^2=r^2
(h,k) - the coordinates of the center
r - the radius

\hbox{the center: } A(-3,2) \nh=-3 \n k=2 \n \n\hbox{the equation:} \n(x+3)^2+(y-2)^2=r^2 \n \n\hbox{the circle passes through B(1,3)} \nx=1 \n y=3 \n \Downarrow \n(1+3)^2+(3-2)^2=r^2 \n4^2+1^2=r^2 \n16+1=r^2 \n17=r^2 \n \n\hbox{the equation is:} \n(x+3)^2+(y-2)^2=17

Plug the coordinates of the points into the equation and check:
C(-1,-2) \n(-1+3)^2+(-2-2)^2=17 \n2^2+(-4)^2=17 \n4+16=17 \n20=17 \nnot \ true \n \nD(-6,3) \n(-6+3)^2+(3-2)^2=17 \n(-3)^2+1^2=17 \n9+1=17 \n10=17 \nnot \ true

E(-3,-3) \n(-3+3)^2+(-3-2)^2=17 \n0^2+(-5)^2=17 \n25=17 \nnot \ true \n \nF(-2,6) \n(-2+3)^2+(6-2)^2=17 \n1^2+4^2=17 \n1+16=17 \n17=17 \ntrue

The answer is F(-2,6).

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Answers

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Hope this helps.

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Answers

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Answers

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Learn more about Line segment click;

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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