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# If points A and B are on the y-axis in the figure, what is the area of

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If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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29 Oct 2014, 08:50
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Tough and Tricky questions: Coordinate Geometry.

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2014-10-29_1948.png [ 26.79 KiB | Viewed 4956 times ]
If points A and B are on the y-axis in the figure, what is the area of equilateral triangle ABC ?

(1) The coordinates of point B are (0, 5√3).
(2) The coordinates of point C are (6, 3√3).
[Reveal] Spoiler: OA

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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29 Oct 2014, 10:00
Hint: Use the concept of perpendicular bisector.
Its a good one

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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29 Oct 2014, 13:56
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Well if we only have coordinates of B, then point C could be anywhere on the quadrant and Point A anywhere on Y axis. So 1) not sufficient

If we have coordinates of C, and it is given that A and B are on y axis, then we can conclude that the length of the altitude/height from point C to the base would be the X coordinate of C $$(3\sqrt{3})$$
So length of height =$$\sqrt{3}$$/2 * side a.
Thus side a would be 6.
From the side length we can find out area of equilateral triangle from formula $$\sqrt{3}$$/4 * a^2
Thus 2) is sufficient.

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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12 Jan 2015, 10:15
PathFinder007 wrote:
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Attachment:
2014-10-29_1948.png
If points A and B are on the y-axis in the figure, what is the area of equilateral triangle ?

(1) The coordinates of point B are (0, 5√3).
(2) The coordinates of point C are (6, 3√3).

HI Bunuel,

Thanks

Consider Statement A : we have coordinates of B but no info is given on C or A, hence not sufficient.

Consider Statement B : we have Coordinates of C (6 , 3_/3)
now x coordinate means perpendicular distance of that point to Y axis which is nothing but height of Triangle
so we know height is 6
we can get side from height and so area.

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If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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13 Jan 2015, 02:16
Rephrased question what the lenght of side of triangleis is, because in equilateral triangle A=a^2*(√3/4), where a is a side

St.1. The coordinates of point B are (0, 5√3). No information about any side. INSUFFICIENT

St.2. The coordinates of point C are (6, 3√3). No direct information about side, but we know that altitude and median=6. So, half of the side is 6/√3. SUFFICIENT

B

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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15 Jan 2015, 01:01
Area of equilateral triangle can be arrived if we have length of one side or one height or...due to its symmetrical properties

Stat1: doesnt give us any unique value (neither side/height/...)
=> no sufficient
Stat2: Gives height straight away...i.e using the (x coordinate of the point C) => we can arrive at area of traingle =>stat 2 is sufficient=>
Ans is B

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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16 Jan 2016, 17:48
from statatement 1 , we coordinate points of B(0,5root3).
It is insufficient to calcualte area of equilateraltriangle.

statement 2:

co ordintates of point C (6,3root3).

draw altitude from point C on A and B line segment.

Both points A and B are on yaxis. then x=0. then, drawn altitude from C to AB is (0,3root3)

then height is 6.
we know altitude or height of equilateral triangle is root3/2*a. then we can find side and area also.
Option B is correct

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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23 Feb 2016, 10:47
Psiva00734

hello, Thank you for the explanation. I understand that the height of this trianble is 6, However, I don't understand how to get the distance from A to AB/2 (this mean half way to point B). To get this wouldn't we have to know the y - distance from point (0,0) to A?

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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25 Feb 2016, 21:35
nzk5053 wrote:
Psiva00734

hello, Thank you for the explanation. I understand that the height of this trianble is 6, However, I don't understand how to get the distance from A to AB/2 (this mean half way to point B). To get this wouldn't we have to know the y - distance from point (0,0) to A?

hi nzk503,
In equilateral traingle
three sides are equal
we know altitude is root3/2a

here altitude is 6.= root3/2a=6
then a= 4root3.

In triangle , the line joining drawn from midpoint of a side pass through opposite vertex is called median and it divide trinagle into two equal areas.

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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17 Jul 2016, 07:46
navkaran wrote:
Well if we only have coordinates of B, then point C could be anywhere on the quadrant and Point A anywhere on Y axis. So 1) not sufficient

If we have coordinates of C, and it is given that A and B are on y axis, then we can conclude that the length of the altitude/height from point C to the base would be the X coordinate of C $$(3\sqrt{3})$$
So length of height =$$\sqrt{3}$$/2 * side a.
Thus side a would be 6.
From the side length we can find out area of equilateral triangle from formula $$\sqrt{3}$$/4 * a^2
Thus 2) is sufficient.

I think there is a small mistake in your calculation. Just wanted to correct so that others don't get confused.

X coordinate of the the point C is 6 and not 3√3

equating this to 6, we get side a is equal to 4√3. And using this we can get the area.

P.S : There is no need of to calculate while solving this question till the time you know you have enough information to get the length of one side.

Thanks and Regards,

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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink]

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22 Sep 2017, 07:14
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Re: If points A and B are on the y-axis in the figure, what is the area of   [#permalink] 22 Sep 2017, 07:14
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