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655-705 (Hard)|   Geometry|      
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Bunuel
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Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1. 13 Jun 2022, 03:45
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Difficulty:

65% (hard)

Question Stats:

52% (02:14) correct 48% (03:09) wrong based on 33 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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Distinct points A, B, C, and D lie on a line, with AB = BC = CD = 1. 13 Jun 2022, 08:24
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Bunuel
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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Area is a function of base and height. In the attached drawing, we will need to make the base on one of the two lines and the height will be the distance between them. The height remains constant regardless which three points we pick. How many options do we have for the length of the base? The base could be 1, 2, or 3. It can't be longer than 3, shorter than 1, or anything between 1 and 3 other than 2. So, there are a three options for the base and one option for the height. 3*1 = 3.

Answer choice A.
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