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Points A, B, and, C have xy-coordinates (2,0), (8,12), and (

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Intern
Joined: 14 Mar 2013
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GMAT Date: 12-03-2013
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Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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19 Nov 2013, 03:19
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Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction of the area of triangle ABC is the area of triangle XYZ?

(A) 1/9
(B) 1/8
(C) 1/6
(D) 1/5
(E) 1/3
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Joined: 25 Oct 2013
Posts: 143
Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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19 Nov 2013, 03:33
If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore

Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4

dividing area of XYZ with that of ABC gives 1/9.

Hope it helps.
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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19 Nov 2013, 03:33
ABC is a triangle with base = 12 units and height = 12 units

Area = 0.5*base*height = 0.5*12*12 = 72

XYZ is a triangle with base = 4 units and height = 4 units

Area = 0.5*base*height = 0.5*4*4 = 8

Fraction = 8/72 = 1/9
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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19 Nov 2013, 03:39
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Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively.

Area of triangle in coordinate plane is

$$1/2 *[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]$$...

The area of ABC will be 72 and area of xyz will be 8..

Fraction : 8/72= 1/9

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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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02 Sep 2015, 08:08
How do I get heights and bases of triangle ABC and XYZ as 12 and 4 respectively?
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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02 Sep 2015, 08:15
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ShristiK wrote:
How do I get heights and bases of triangle ABC and XYZ as 12 and 4 respectively?

If you plot the points in XY plane, you will see that the height of triangle ABC = y-coordinate of B = 12, the other 2 points lie on the X axis and thus can not give the height of the triangle.

Similarly, height of triangle XYZ = y-coordinate of Y = 4, the other 2 points lie on the X axis and thus can not give the height of the triangle.

Hope this helps.
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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02 Sep 2015, 09:17
Thanks a lot!
I really need to read the question carefully. I've been plotting (14,0) and (10,0) as (0,14) and (0,10) all this time!
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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22 Oct 2016, 09:58
I'd recommend plotting this one. It's very easy to see that they are equilateral triangles & you can calculate the area of each and compare.

Area ABC = 36sqrt(3)
Area XYZ = 4sqrt(3)

Ratio of XYZ: ABC = 1/9
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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (  [#permalink]

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Re: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (   [#permalink] 18 Aug 2018, 19:04
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