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Re: co-ordinate geometry question [#permalink]
16 May 2011, 12:01

1

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Statement 1 : Not sufficient. We know the position of B, but not the position of A. Thus we can not calculate the value of AB.

Statement 2: Sufficient. We know the position of C => we know the perpendicular distance from the line AB => we know the altitude of the triangle => we have the area.

Re: co-ordinate geometry question [#permalink]
16 May 2011, 12:29

Stmt1 . We know only one co-ordinate. we don't know altitude, base or one side of triangle. Hence insufficient.

Stmt2: We know altitude when draw from C to opposite base is 6. Also this altitude will bisect the angle ACB making each angle 30. So cos30 = altitude/CA {imagine a line from C to AB} \sqrt{3}/2=6/CA

CA= 12/\sqrt{3}. We know one side of EQUILATERAL triangle.

Apply formula Area of equilateral triangle= s^2 * \sqrt{3}/4 = (12/\sqrt{3})^2* \sqrt{3}/4 = 12\sqrt{3} Hence sufficient.

OA B. _________________

My dad once said to me: Son, nothing succeeds like success.

Last edited by jamifahad on 16 May 2011, 12:53, edited 1 time in total.

Re: co-ordinate geometry question [#permalink]
16 May 2011, 19:11

a the distance from origin to A is not known.Hence side of the equilateral triangle cannot be calculated. Not sufficient.

b C has x coordinate = 6 = altitude of equilateral triangle y coordinate = 3* 3^(1/2) also does not account for the distance from origin to A.

however altitude a = 6 means side = 6*2/3^(1/2) as in a triangle with angle 60 deg sides are in the ratio 3^(1/2)(perpendicular):1 (base):2(hypotenuse)