{"@context":"https://schema.org/","@type":"Quiz","name":"

A circle in the $xy$-plane has equation $(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-54"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

A circle in the $xy$-plane has equation $(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?

","comment":{"@type":"Comment","text":"

Choice D is correct. The circle with equation $(x+3)^{2}+(y-1)^{2}=25$ has center $(-3,1)$ and radius 5. For a point to be inside of the circle, the distance from that point to the center must be less than the radius, 5. The distance between $(3,2)$ and $(-3,1)$ is $\\sqrt{(-3-3)^{2}+(1-2)^{2}}=\\sqrt{(-6)^{2}+(-1)^{2}}=\\sqrt{37}$, which is greater than 5. Therefore, $(3,2)$ does NOT lie in the interior of the circle.

Choice A is incorrect. The distance between $(-7,3)$ and $(-3,1)$ is $\\sqrt{(-7+3)^{2}+(3-1)^{2}}=\\sqrt{(-4)^{2}+(2)^{2}}=\\sqrt{20}$, which is less than $5$, and therefore $(-7,3)$ lies in the interior of the circle. Choice B is incorrect because it is the center of the circle. Choice C is incorrect because the distance between $(0,0)$ and $(-3,1)$ is $\\sqrt{(0+3)^{2}+(0-1)^{2}}=\\sqrt{(3)^{2}+(1)^{2}}=\\sqrt{8}$, which is less than $5$, and therefore $(0,0)$ in the interior of the circle.

"},"encodingFormat":"text/markdown","text":"

A circle in the $xy$-plane has equation $(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$(-7,3)$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$(-3,1)$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

\$(0,0)\$

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$(3,2)$

","comment":{"@type":"Comment","text":"

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