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Bunuel
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 29 Jun 2021, 07:15
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D
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65% (02:00) correct 35% (02:09) wrong based on 156 sessions

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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Which of the following could be the co-ordinates of the third vertex?

(A) (-4, 3)
(B) ( -4, -4√3)
(C) (4, 3)
(D) (4, -3)
(E) (4, 4√3)
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D
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 23 Aug 2021, 17:34
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I just plotted the points and extended a horizontal line from point (-4,-3) to (4,-3) in the IInd quadrant to create an equidistant point.

Any further explanation will be helpful!
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 29 Aug 2021, 03:55
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Can anyone explain this question?
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 29 Aug 2021, 06:48
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we have 2 points of an equilateral triangle and we need to find the third point

obviously the third point should be equidistant from these 2 points so you can write an equation quickly by assuming the 3rd point is (x,y) using distance formula (x-x1)^2 + (y-y1)^2 =(x-x2)^2 + (y-y2)^2

(x- 0)^2 +(y-4√3 + 3)^2 =(x + 4)^2 +(y+3)^2

quickly solving this

=> x^2 + y^2 +2y(3-4√3 ) +(3-4√3 )^2 = x^2 +16+ 8x+y^2+9+6y

=> -8y√3 +48-24√3 = 16+ 8x

=> 8x+8y√3+ 24√3-32=0

=> x+y√3 = 4-3√3

now you can substitute each answer choice and check
and one of the quick way to do that is
as all answer choices have x as an integer, we can only cancel out the -3√3 in RHS with y√3 in LHS (comparing the irrationals in both sides ) so your y can be -3 which is option D

(A) (-4, 3)
(B) ( -4, -4√3)
(C) (4, 3)
(D) (4, -3)
(E) (4, 4√3)
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 04 Mar 2024, 03:49
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sahiba96
we have 2 points of an equilateral triangle and we need to find the third point

obviously the third point should be equidistant from these 2 points so you can write an equation quickly by assuming the 3rd point is (x,y) using distance formula (x-x1)^2 + (y-y1)^2 =(x-x2)^2 + (y-y2)^2

(x- 0)^2 +(y-4√3 + 3)^2 =(x + 4)^2 +(y+3)^2

quickly solving this

=> x^2 + y^2 +2y(3-4√3 ) +(3-4√3 )^2 = x^2 +16+ 8x+y^2+9+6y

=> -8y√3 +48-24√3 = 16+ 8x

=> 8x+8y√3+ 24√3-32=0

=> x+y√3 = 4-3√3

now you can substitute each answer choice and check
and one of the quick way to do that is
as all answer choices have x as an integer, we can only cancel out the -3√3 in RHS with y√3 in LHS (comparing the irrationals in both sides ) so your y can be -3 which is option D

(A) (-4, 3)
(B) ( -4, -4√3)
(C) (4, 3)
(D) (4, -3)
(E) (4, 4√3)
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­Can we use a less time-consuming method? 
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(0, 4√3 - 3) and (-4, -3) are vertices of an equilateral triangle. Whi 14 May 2025, 05:52
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Hi, I just tried to analyze the possible less time consuming solution from my end.
Just roughly plotting the points, one point lies on +y axis and another point in Quad 3. So the 3rd point should lie either in 4th Quad or 2nd
So possible solution could be A or D. Now just calculate the length of sides : D will be the answer.
Thanks!!
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