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In the xy-plane, the vertices of an equilateral triangle are (0, 1)
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27 Jun 2024, 11:59
27 Jun 2024, 11:59
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In the xy-plane, the vertices of an equilateral triangle are (0, 1), (4, 3), and (a, b).
Which of the following statements individually provides) sufficient additional information to determine the vertex (a, b)?
A. \(2b - a > 2\)
B. \(a < 2\)
C. \(a^2 + (b - 1)^2 = 20\)
Which of the following statements individually provides) sufficient additional information to determine the vertex (a, b)?
A. \(2b - a > 2\)
B. \(a < 2\)
C. \(a^2 + (b - 1)^2 = 20\)
Re: In the xy-plane, the vertices of an equilateral triangle are (0, 1)
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27 Jun 2024, 15:47
27 Jun 2024, 15:47
Expert Reply
In the xy plane we do have a triangle of which boundaries are the green side and the purple side according to the stem.
Now the third side must be the yellow one.
To know which statement of the three is useful to have enough information basically we need the a value of the coordinate point or the x (which is the same)
I.E C for example to be 20 our a should be 2 and our b should be 5 so the point is (2,5) and this clearly is impossible because we would have a point NOT on the yellow line
Instead with A and B to have a value < 2 a and b should be number less then 4 and 1, respectively
A and B are the only answer choices useful to have the yellow line or the third vertex
xyplane.png [ 1.69 KiB | Viewed 839 times ]
Now the third side must be the yellow one.
To know which statement of the three is useful to have enough information basically we need the a value of the coordinate point or the x (which is the same)
I.E C for example to be 20 our a should be 2 and our b should be 5 so the point is (2,5) and this clearly is impossible because we would have a point NOT on the yellow line
Instead with A and B to have a value < 2 a and b should be number less then 4 and 1, respectively
A and B are the only answer choices useful to have the yellow line or the third vertex
Attachment:
xyplane.png [ 1.69 KiB | Viewed 839 times ]
gmatclubot
Re: In the xy-plane, the vertices of an equilateral triangle are (0, 1) [#permalink]
27 Jun 2024, 15:47
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