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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In the xy-coordinate system, rectangle ABCD is inscribed ##### This topic has 2 expert replies and 0 member replies ### Top Member ## In the xy-coordinate system, rectangle ABCD is inscribed ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2 + y^2 = 25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15, what is the area of rectangle ABCD? A. 15 B. 30 C. 40 D. 45 E. 50 OA B Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15342 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2 + y^2 = 25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15, what is the area of rectangle ABCD? A. 15 B. 30 C. 40 D. 45 E. 50 xÂ²+yÂ² = rÂ² is the equation for a circle with its center at the origin and a radius of r. Thus, xÂ²+yÂ² = 25 is a circle with a center at the origin and a radius of 5. The information in the prompt yields the following figure: OB is a radius and thus has a length of 5. Given the GMAT's love of special triangles, it is likely that triangle BOE is a 3-4-5 triangle, implying that B is located either at (-3, 4) or (-4, 3). B lies on the line y=3x+15. If we plug x=-4 into y=3x+15, we get y=3, implying that (-4, 3) lies on y=3x+15. Thus, B is located at (-4, 3). Since BE=3, the area of triangle ABC = (1/2)bh = (1/2)(CA)(BE) = (1/2)(10)(3) = 15. Since the triangle ABC is 1/2 of rectangle ABCD, we get: ABCD=30. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2 + y^2 = 25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15, what is the area of rectangle ABCD? A. 15 B. 30 C. 40 D. 45 E. 50 OA B Source: GMAT Prep The equation of the circle x^2 + y^2 = 25 suggests that the given circle has its center at the origin and radius equal to âˆš25 = 5. Thus, AD = 2*5 = 10 = Diameter. Since AD lies on the X-axis, the coordinate of A = (-5, 0) and the coordinate of D = (5, 0). Now we are given that vertex B lies on the quadrant II and n the circle. Thus, the point must satisfy the equation x^2 + y^2 = 25 and the line y = 3x + 15. Plugging in the value of y = 3x + 15 in x^2 + y^2 = 25, we get x = -5 or -4; the corresponding value of y are 0 and 3, respectively. Thus, B can be (-5, 0) or (-4, 3). Again, the vertex B lies on the quadrant II, the coordinate of B would be (-4, 3). Area of the rectangle ABCD = 2 * Area of the triangle ABC Area of the triangle ABC = 1/2 * (Perpendicular dropped from vertex B on AD) * (Base AD) = 1/2 * (Y-coordinate of vertex B) * 10 = 1/2 * 3 * 10 = 15 Area of the rectangle ABCD = 2 * Area of the triangle ABC = 2 * 15 = 30 The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GRE Manhattan | ACT Tutoring Houston | SAT Prep Courses Seattle | Charlotte IELTS Tutoring | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • FREE GMAT Exam Know how you'd score today for$0

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