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02 Jul 2020, 02:31
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E
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Difficulty:
95%
(hard)
Question Stats:
35% (02:22) correct
65%
(02:39)
wrong
based on 81
sessions
History
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Not Attempted Yet
Point A(–4, 2) and Point B(2, 4) lie in the xy-coordinate plane. If point C(p, q) lies in the first quadrant, where p < 2 and q < 4, which of the following could be the area of triangle ABC?
I. 1.1
II. 3.9
III. 11.9
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
I. 1.1
II. 3.9
III. 11.9
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
02 Jul 2020, 05:05
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line joining points (-4,2) and (2,4) is \(y-4 = \frac{1}{3} (x-2)\) or \(3y-x-10=0\)
Maximum possible distance of a point in the given range from above mentioned line \(= \frac{|3*0-2-10|}{\sqrt{3^2+1^2}}\)
Range of the area of possible triangles =
\(\frac{1}{2}* 0* √40 < A < \frac{1}{2} * \frac{12}{√10} *√40\)
0 < A < 12
E
Maximum possible distance of a point in the given range from above mentioned line \(= \frac{|3*0-2-10|}{\sqrt{3^2+1^2}}\)
Range of the area of possible triangles =
\(\frac{1}{2}* 0* √40 < A < \frac{1}{2} * \frac{12}{√10} *√40\)
0 < A < 12
E
Bunuel
02 Jul 2020, 09:08
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Point C(p,q) is bound inside figure DOFB
Let AB be the base of every triangle that can be formed using points A, B, and C.
The triangle with minimum area will have its height(distance from AB) close to zero. So the minimum area of the triangle will be greater than but close to 0.
The triangle with maximum area will have the maximum height. From the figure we can see that the maximum height occurs when C coincides with F(2,0).
h1 < h2 < h3
Thus, triangle AFB will have the maximum area. Area of triangle AFB = 0.5*4*6 = 12. Since p < 2 and q < 4, the maximum area of ABC will be less than 12.
So, 0 < Area of ABC < 12.
All 3 values are possible in this range.
Ans: E
Let AB be the base of every triangle that can be formed using points A, B, and C.
The triangle with minimum area will have its height(distance from AB) close to zero. So the minimum area of the triangle will be greater than but close to 0.
The triangle with maximum area will have the maximum height. From the figure we can see that the maximum height occurs when C coincides with F(2,0).
h1 < h2 < h3
Thus, triangle AFB will have the maximum area. Area of triangle AFB = 0.5*4*6 = 12. Since p < 2 and q < 4, the maximum area of ABC will be less than 12.
So, 0 < Area of ABC < 12.
All 3 values are possible in this range.
Ans: E
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