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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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Bunuel
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If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  29 Oct 2014, 08:50
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Tough and Tricky questions: Coordinate Geometry.





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).

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navkaran
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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  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] New post  29 Oct 2014, 10:00
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Hint: Use the concept of perpendicular bisector. :-D
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] New post  12 Jan 2015, 10:15
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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,

Could you please provide your comments on this.

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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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  13 Jan 2015, 02:16
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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] New post  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] New post  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] New post  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] New post  25 Feb 2016, 21:35
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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.
Hope i clarify your doubt
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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  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,
Shradha
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Re: If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  01 Mar 2020, 09:03
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.





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).

Show Spoiler
Attachment:
2014-10-29_1948.png


#1
The coordinates of point B are (0, 5√3).
clearly insufficient
as we dont know the distance from origin
#2
The coordinates of point C are (6, 3√3).
the height of ∆ equilateral is 6 ;
6=√3/2 * a ; a= 12/√3 ;
sufficient to find area ;
IMO B
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If points A and B are on the y-axis in the figure, what is the area of [#permalink] New post  25 Jul 2021, 22:46
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1) The coordinates of point B are (0, 5√3).
clearly insufficient

(2) The coordinates of point C are (6, 3√3).
it is given that A and B are on y axis,
height from point C to the base would be the X coordinate of C (3√3)
So length of height =√3/2 * a.
Thus side a would be 6.
From the side length we can find out area of equilateral triangle from formula 3√3/4 * a^2
Thus sufficient
Therefore IMO 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] New post  07 Oct 2023, 23:38
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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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