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# Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1.

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1.  [#permalink]

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28 Mar 2019, 23:50
00:00

Difficulty:

55% (hard)

Question Stats:

47% (02:13) correct 53% (01:44) wrong based on 15 sessions

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Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1. Points E and F lie on a second line, parallel to the first, with EF = 1. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

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Re: Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1.  [#permalink]

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29 Mar 2019, 00:16
1
Triangles can be formed by either two points from a, b, c, d and one from e, f or two of e f and one from a, b, c, d.
In each of the triangles, height is same. I. E. Distance between two lines ad and ef. Only base changes when base=ab, ac and ad. With 1, 2, 3 units. Ef=ab=bc=cd= 1 unit.
So, there are 3 possibilities for the area.
Imo, option a.

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Re: Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1.   [#permalink] 29 Mar 2019, 00:16
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