{"id":"cb_question_bank:dae7aedc-591e-4058-baf2-bd52f1608561","source_id":"cb_question_bank","source_item_id":"dae7aedc-591e-4058-baf2-bd52f1608561","external_id":null,"ibn":"10166-DC","question_id":"acd30391","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A circle in the xy -plane has equation open parenthesis, x plus 3, close parenthesis, squared, plus, open parenthesis, y minus 1, close parenthesis, squared, equals 25 . Which of the following points does NOT lie in the interior of the circle?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A circle in the <span class=\"italic \">xy</span>-plane has equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/caca8cc6359380c49228eef3348c14cd372f29bf8c7a18aa12ead56d6c949c5e\" alt=\"open parenthesis, x plus 3, close parenthesis, squared, plus, open parenthesis, y minus 1, close parenthesis, squared, equals 25\"></span>.</span> Which of the following points does NOT lie in the interior of the circle?</p>\n","rationale_html":"<p>Choice D is correct. The circle with equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/caca8cc6359380c49228eef3348c14cd372f29bf8c7a18aa12ead56d6c949c5e\" alt=\"open parenthesis, x plus 3, close parenthesis, squared, plus, open parenthesis, y minus 1, close parenthesis, squared, equals 25\"></span> has center <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7367e0fb0695bec2a4da79b9e4b468f8362f8eba63831abfd04d33b32635fac3\" alt=\"with coordinates negative 3 comma 1\"></span> 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 <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5f7e71dbdebd336532049c47818839093c3d5179d95c9f72520f8bd9f5e53c3\" alt=\"the point with coordinates 3 comma 2\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7367e0fb0695bec2a4da79b9e4b468f8362f8eba63831abfd04d33b32635fac3\" alt=\"the point with coordinates negative 3 comma 1\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a191f933901a48e5c70a4b26d3812af5f1840bcfa8b116f81c30e9f046d93b55\" alt=\"the square root of, open parenthesis, negative 3 minus 3, close parenthesis, squared, plus, open parenthesis, 1 minus 2, close parenthesis, squared, end root, equals, the square root of, open parenthesis, negative 6, close parenthesis, squared, plus, open parenthesis, negative 1, close parenthesis, squared, end root, which equals the square root of 37\"></span>, which is greater than 5. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5f7e71dbdebd336532049c47818839093c3d5179d95c9f72520f8bd9f5e53c3\" alt=\"the point with coordinates 3 comma 2\"></span> does NOT lie in the interior of the circle.</p><p>Choice A is incorrect. The distance between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e11e17c4d518ec6cbb62ac4c4d6c62385e64bf63ca56008672251f767b041a39\" alt=\"the point with coordinates negative 7 comma 3\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7367e0fb0695bec2a4da79b9e4b468f8362f8eba63831abfd04d33b32635fac3\" alt=\"the point with coordinates negative 3 comma 1\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce2b24a7d1a58edc2bd2b042012185ec1211eb20742357586fd7b3fd837a0514\" alt=\"the square root of, open parenthesis, negative 7 plus 3, close parenthesis, squared, plus, open parenthesis, 3 minus 1, close parenthesis, squared, end root, equals, the square root of, open parenthesis, negative 4, close parenthesis, squared, plus, open parenthesis, 2, close parenthesis, squared, end root, which equals the square root of 20\"></span>, which is less than 5, and therefore <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e11e17c4d518ec6cbb62ac4c4d6c62385e64bf63ca56008672251f767b041a39\" alt=\"the point with coordinates negative 7 comma 3\"></span> 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 <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d9546145044d67f4c5d0648e8663a351f932cd21526a7309901dbb9e25d27fb\" alt=\"the point with coordinates 0 comma 0\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7367e0fb0695bec2a4da79b9e4b468f8362f8eba63831abfd04d33b32635fac3\" alt=\"the point with coordinates negative 3 comma 1\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2e3e7a4ad78d4678bf9935feacb1279cb3839d0619202e880867cb512dab1691\" alt=\"the square root of, open parenthesis, 0 plus 3, close parenthesis, squared, plus, open parenthesis, 0 minus 1, close parenthesis, squared, end root, equals, the square root of, open parenthesis, 3, close parenthesis, squared, plus open parenthesis, 1, close parenthesis, squared, end root, which equals the square root of 8\"></span>, which is less than 5, and therefore <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d9546145044d67f4c5d0648e8663a351f932cd21526a7309901dbb9e25d27fb\" alt=\"the point with coordinates 0 comma 0\"></span> in the interior of the circle.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/310f25d00624a433ea4ea547e20d0f3332e3f1a5b164f34b513aacc1e3f73145\" alt=\"negative 7 comma 3\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/de9386263ff059078e5be3dd5027702a12d5bb2e928e1544a0fd63e89541f408\" alt=\"negative 3 comma 1\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/82a99a9b3da4fb5e4999f1db2e4d8ad24650aeea14ee3f73362575159b3c8cd6\" alt=\"zero comma zero\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/72898025e98a3dac1c05acd5fee8a046e3180a2d0052db393bce788968bba6c2\" alt=\"3 comma 2\"></span></span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}