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If \(ABC\) is an equilateral triangle, \(AC\) lies on the

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If \(ABC\) is an equilateral triangle, \(AC\) lies on the

by BTGmoderatorLU » Fri Oct 04, 2019 8:50 am
Source: Economist GMAT

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If \(ABC\) is an equilateral triangle, \(AC\) lies on the \(x-\)axis and \(A\) is closer to the origin than \(C\), what are the coordinates of point \(A\)?

1) The coordinates of point \(C\) are \((6,0)\)
2) The coordinates of point \(B\) are \((4, 2\sqrt{3})\)

The OA is B
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Fri Oct 04, 2019 10:43 pm
BTGmoderatorLU wrote:Source: Economist GMAT

Image

If \(ABC\) is an equilateral triangle, \(AC\) lies on the \(x-\)axis and \(A\) is closer to the origin than \(C\), what are the coordinates of point \(A\)?

1) The coordinates of point \(C\) are \((6,0)\)
2) The coordinates of point \(B\) are \((4, 2\sqrt{3})\)

The OA is B
Let's take each statement one by one.

1) The coordinates of point \(C\) are \((6,0)\).

Can't get the coordinates of point \(A\). Insufficient.

2) The coordinates of point \(B\) are \((4, 2\sqrt{3})\).

Drop a perpendicular from point B on AC. Say it meets AC at Point B'. The perpendicular will divide AC into two equal segments. Say AB' = x; thus, AC = 2x. Also, BB' = 2√3.

In ∆ABB', we have (AB)^2 = (BB')^2 + (AB')^2

Thus, (2x)^2 = (2√3)^2 + x^2 => 4x^2 = 12 + x^2 => 3x^2 = 12 => x = 2.

Thus, the coordinates of point \(A\) are (2, 0). Sufficient.

The correct answer: B

Hope this helps!

-Jay
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