{"id":"cb_practice_pdf:t5-math-m2-q26","source_id":"cb_practice_pdf","source_item_id":"t5-math-m2-q26","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":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-5","module_number":2,"position":26,"stem":"−1,1 A circle in the xy-plane has its center at. Line t is tangent to this circle at the point 5,−4. Which of the following points also lies on line t? 0,","stimulus":"","stimulus_html":null,"stem_html":"<p>−1,1 A circle in the xy-plane has its center at. Line t is tangent to this circle at the point 5,−4. Which of the following points also lies on line t? 0,</p>","rationale_html":"<p>-1,1 Choice C is correct. It’s given that the circle has its center at ^ h and that 5,-4 line t is tangent to this circle at the point ^ h. Therefore, the points -1,1 5,-4 ^ h and ^ h are the endpoints of the radius of the circle at the point of tangency. The slope of a line or line segment that contains the points ^a,bh and d - b -1,1 5,-4 ^c,dh can be calculated as - . Substituting ^ h for ^a,bh and ^ h for d - b c a -4-1 -5 ^c,dh in the expression - yields 5- -1, or 6. Thus, the slope of this radius is -5 c a ^ h 6. A line that’s tangent to a circle is perpendicular to the radius of the circle at the point of tangency. It follows that line t is perpendicular to the radius at the 5,-4 point ^ h, so the slope of line t is the negative reciprocal of the slope of this -5 6 6 radius. The negative reciprocal of 6 is 5. Therefore, the slope of line t is 5. Since the slope of line t is the same between any two points on line t, a point lies 5,-4 6 on line t if the slope of the line segment connecting the point and ^ h is 5. 10,2 5,-4 Substituting choice C, ^ h, for ^a,bh and ^ h for ^c,dh in the expression - -4-2 6 10,2 d b - yields 5-10, or 5. Therefore, the point ^ h lies on line t. c a 49 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 0,6 Choice A is inco6rrect. The slope of the line segment connecting b 5l and -4- 5,-4 5 -26 6 ^ h is 5-0 , or 25, not 5. Choice B is incorrect. The slope of the line 4,7 5,-4 -4-7 - 6 segment connecting ^ h and ^ h is 5-4 , or 11, not 5. Choice D is 11,1 5,-4 -4-1 incorrect. The slope of the line segment connecting ^ h and ^ h is 5-11, 5 6 or 6, not 5.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>6/5 4,7</p>","ord":0},{"label":"B","content_html":"","ord":1},{"label":"C","content_html":"<p>10,2</p>","ord":2},{"label":"D","content_html":"<p>11,1 STO</p>","ord":3}],"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}}