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In a rectangular coordinate plane, AB is the diameter of a circle and
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01 Jun 2017, 00:15
Question Stats:
66% (03:09) correct 34% (02:59) wrong based on 107 sessions
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In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C? A. (0, 2\(\sqrt{2}\)) B. (1, 2\(\sqrt{2}\)) C. (\(\sqrt{2}\),2) D. (2,\(\sqrt{2}\)) E. (2\(\sqrt{2}\),1)
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In a rectangular coordinate plane, AB is the diameter of a circle and
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01 Jun 2017, 01:40
niteshwaghray wrote: In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C?
A. (0, 2\(\sqrt{2}\)) B. (1, 2\(\sqrt{2}\)) C. (\(\sqrt{2}\),2) D. (2,\(\sqrt{2}\)) E. (2\(\sqrt{2}\),1) Attachment:
Capture.PNG [ 12.32 KiB  Viewed 2007 times ]
We have \(AB=6 \implies R = 3\). \(I\) is the center of that circle, then we have \(I(2,0)\) The equation of that circle is \((I): \; \; (x2)^2 + y^2 = 3^2\) The coordinates of \(C(x_C, y_C)\). We have \((x_C2)^2 + y_C^2 = 9\) Also, we have \(S_{ABC}=6\sqrt{2} \implies \frac{AB \times y_C}{2}=6\sqrt{2} \\ \implies y_C=2\sqrt{2} \implies y_C^2=8 \) \(\implies (x_C2)^2 = 1 \implies x_C = 3\) or \(x_C = 1\). Only choice B fits the roots. B is the correct answer.
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In a rectangular coordinate plane, AB is the diameter of a circle and
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25 Sep 2018, 11:05
Analysis (51 seconds): Draw out a rough estimation of the coordinate plane, mark the points and draw a circle. Notice that I can use the area of a triangle to get a value for Y for point C. Strategy: Find Y, Eliminate Find Y (35 seconds)\(Ta = \frac{1}{2}*b*h\) \(\frac{1}{2}*6*h = 6\sqrt{2}\) \(3*h = 6\sqrt{2}\) \(Y = 6\sqrt{2} / 3\) \(Y = 2\sqrt{2}\) Eliminate (20 seconds)A: With only two choices left, logically it can only be the one closest to the centre of the circle so eliminate A.  B: Correct Answer
C: Wrong YD: Wrong Y E: Wrong Y Answer: BTime: 1:46



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Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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17 Mar 2019, 13:34
jameslewis wrote: Analysis (51 seconds): Draw out a rough estimation of the coordinate plane, mark the points and draw a circle. Notice that I can use the area of a triangle to get a value for Y for point C. Strategy: Find Y, Eliminate Find Y (35 seconds)\(Ta = \frac{1}{2}*b*h\) \(\frac{1}{2}*6*h = 6\sqrt{2}\) \(3*h = 6\sqrt{2}\) \(Y = 6\sqrt{2} / 3\) \(Y = 2\sqrt{2}\) Eliminate (20 seconds)A: With only two choices left, logically it can only be the one closest to the centre of the circle so eliminate A.  B: Correct Answer
C: Wrong YD: Wrong Y E: Wrong Y Answer: BTime: 1:46 though you are getting the correct answer , but i guess the method is wrong as AB is the diameter of the circle and point C on the circle so <C =90 deg so , AB will be the hypotenuse not the base of the triangle , as you have used it as base of 6 units to eliminate answer choices let me know if i am wrong



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Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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24 Nov 2019, 11:36
broall wrote: niteshwaghray wrote: In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C?
A. (0, 2\(\sqrt{2}\)) B. (1, 2\(\sqrt{2}\)) C. (\(\sqrt{2}\),2) D. (2,\(\sqrt{2}\)) E. (2\(\sqrt{2}\),1) Attachment: Capture.PNG We have \(AB=6 \implies R = 3\). \(I\) is the center of that circle, then we have \(I(2,0)\) The equation of that circle is \((I): \; \; (x2)^2 + y^2 = 3^2\) The coordinates of \(C(x_C, y_C)\). We have \((x_C2)^2 + y_C^2 = 9\) Also, we have \(S_{ABC}=6\sqrt{2} \implies \frac{AB \times y_C}{2}=6\sqrt{2} \\ \implies y_C=2\sqrt{2} \implies y_C^2=8 \) \(\implies (x_C2)^2 = 1 \implies x_C = 3\) or \(x_C = 1\). Only choice B fits the roots. B is the correct answer. Hi, broall , I did not get the equation of the circle from your explanation. Would you be so kind to explain how you derive it? Thanks.



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Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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08 Dec 2019, 23:11
Quote: Eliminate (20 seconds) A: With only two choices left, logically it can only be the one closest to the centre of the circle so eliminate A. B: Correct Answer C: Wrong Y D: Wrong Y E: Wrong Y How did you eliminate option A?? How did you arrive at x co ordinate as 1? it could have also been 0 and y co ordinate as 2 root 2 Can you pls explain



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Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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08 Dec 2019, 23:57
niteshwaghray wrote: In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C?
A. (0, 2\(\sqrt{2}\)) B. (1, 2\(\sqrt{2}\)) C. (\(\sqrt{2}\),2) D. (2,\(\sqrt{2}\)) E. (2\(\sqrt{2}\),1) AB = 6 units When AB is the base of the triangle and h is height of the triangle Area = (1/2) * AB * h = 6\sqrt{2} h = 2\sqrt{2} Options C, D and E are eliminated option A not possible as it is lying on the x axis B is correct.



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Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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09 Dec 2019, 03:49
kapil, A is lying on the y axis. I still don't understand why eliminate A Posted from my mobile device




Re: In a rectangular coordinate plane, AB is the diameter of a circle and
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