{"id":"cb_question_bank:ada9b5f8-cda4-4f42-8048-f8fa600d61f2","source_id":"cb_question_bank","source_item_id":"ada9b5f8-cda4-4f42-8048-f8fa600d61f2","external_id":null,"ibn":"11301-DC","question_id":"981275d2","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates 10 comma negative 5 . If line segment P Q is a diameter of the circle, what are the coordinates of point Q ?","stimulus":"Open parenthesis, x minus 6, close parenthesis, squared, plus, open parenthesis, y plus 5, close parenthesis, squared, equals 16","stimulus_html":"
\n\t

\"Open

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\n","stem_html":"

In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates \"10. If \"line is a diameter of the circle, what are the coordinates of point Q ?

\n","rationale_html":"

Choice A is correct. The standard form for the equation of a circle is \"open, where \"the are the coordinates of the center and r is the length of the radius. According to the given equation, the center of the circle is \"the. Let \"x represent the coordinates of point Q. Since point P \"10 and point Q \"x are the endpoints of a diameter of the circle, the center \"with lies on the diameter, halfway between P and Q. Therefore, the following relationships hold: \"the and \"the. Solving the equations for \"x and \"y, respectively, yields \"x and \"y. Therefore, the coordinates of point Q are \"2.

Alternate approach: Since point P \"10 on the circle and the center of the circle \"6 have the same y-coordinate, it follows that the radius of the circle is \"10. In addition, the opposite end of the diameter \"P must have the same y-coordinate as P and be 4 units away from the center. Hence, the coordinates of point Q must be \"2.

Choices B and D are incorrect because the points given in these choices lie on a diameter that is perpendicular to the diameter \"P. If either of these points were point Q, then \"line would not be the diameter of the circle. Choice C is incorrect because \"the is the center of the circle and does not lie on the circle.

 

\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+00:00","options":[{"label":"A","content_html":"

\"2

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\"6

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\"6

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\"6

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