{"id":"cb_practice_pdf:t10-math-m2-q20","source_id":"cb_practice_pdf","source_item_id":"t10-math-m2-q20","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-10","module_number":2,"position":20,"stem":"- - - - -_a_diameter_with - - ~ xy A circle in the -plane has endpoints (2,4) and (2,14). An equation of this (x−2)^2 +(y−9)^2 = circle is r^2, where r is a positive constant. What is the value of r?","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - - -_a_diameter_with - - ~ xy A circle in the -plane has endpoints (2,4) and (2,14). An equation of this (x−2)^2 +(y−9)^2 = circle is r^2, where r is a positive constant. What is the value of r?</p>","rationale_html":"<p>The correct answer is 5. The standard form of an equation of a circle in the - 2+ - 2= 2 xy-plane is ^x hh ^y kh r , where h, k, and r are constants, the coordinates of the center of the circle are ^h,kh, and the length of the radius of the -2 2+ -9 2= 2 circle is r. It′s given that an equation of the circle is ^x h ^y h r . 2,9 Therefore, the center of this circle is ^ h. It’s given that the endpoints of a 2,4 2,14 diameter of the circle are ^ h and ^ h. The length of the radius is the distance from the center of the circle to an endpoint of a diameter of the circle, which can be found using the distance formula, ^x1- x2 h 2+ ^y1- y2 h 2 . 2,9 2,4 Substituting the center of the circle ^ h and one endpoint of the diameter ^ h 2-2 2+ 9-4 2 02+52 in this formula gives a distance of ^ h ^ h , or , which is equivalent to 5. Since the distance from the center of the circle to an endpoint of a diameter is 5, the value of r is 5.</p>","correct_answer":["5"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}