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03 Nov 2021, 05:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:57) correct
39%
(02:24)
wrong
based on 108
sessions
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A circle centered at (4,-1) intersects the x-axis and y-axis at 2 points each. Three points out of the four intercept points are taken to form a triangle. If two vertices of the triangle are (0,-8) and (12,0), which of the following could be the third vertex?
I. (-4,0)
II. (0,-6)
III. (0,6)
A. I only
B. II only
C. III only
D. I&III only
E. I,II & III
I. (-4,0)
II. (0,-6)
III. (0,6)
A. I only
B. II only
C. III only
D. I&III only
E. I,II & III
06 Nov 2021, 00:30
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Bunuel
TWO ways
(I) Radius.
Radius should be equal at all points.
(0,-8): R = \(\sqrt{(4-0)^2+(-1-(-8))^2}=\sqrt{4^2+7^2}=\sqrt{65}\)
(12,0): R = \(\sqrt{(4-12)^2+(-1-0)^2}=\sqrt{8^2+1^2}=\sqrt{65}\)
Let us check the options
I. (-4,0): R = \(\sqrt{(4-(-4))^2+(-1-0)^2}=\sqrt{8^2+1^2}=\sqrt{65}\).......Yes
II. (0,-6): R = \(\sqrt{(4-0)^2+(-1-(-6))^2}=\sqrt{4^2+5^2}=\sqrt{41}\)......No
III. (0,6): R = \(\sqrt{(4-0)^2+(-1-(6))^2}=\sqrt{4^2+7^2}=\sqrt{65}\)......Yes
(II) Logical
Since the intersection will be symmetrical on both sides of the center, the coordinates should be equally distant from center.
Center - (4,-1)
1) Coordinates - (0,-8)
We are looking at x = 0, so -1-(-8) = -1+8 = 7. Thus, the symmetrical point will be -1+7 = 6.........(0,6)
2) Coordinates - (12,0)
We are looking at y = 0, so 4-12 = -8. Thus, the symmetrical point will be 4+(-8) = -4.........(-4,0)
I and III
D
25 Feb 2024, 17:16
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