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In the figure above, a line segment joining the point (3,10) and which

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In the figure above, a line segment joining the point (3,10) and which [#permalink]

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New post 17 Dec 2017, 22:19
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E

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  55% (hard)

Question Stats:

63% (01:45) correct 37% (02:03) wrong based on 51 sessions

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In the figure above, a line segment joining the point (3,10) and which of the following points on the square will separate the square into two regions whose areas are in the ratio 7 to 1?

(A) (11,3)
(B) (11,4)
(C) (11,6)
(D) (11,7)
(E) (11,8)

[Reveal] Spoiler:
Attachment:
2017-12-18_1011.png
2017-12-18_1011.png [ 6.73 KiB | Viewed 344 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, a line segment joining the point (3,10) and which [#permalink]

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New post 17 Dec 2017, 22:26
E

Area of the square = 8*8
=64

To divide the ratio into 7:1 we have to find a point on the vertical side of the square opposite to (3,10) such that the area of the triangle is 8.

Area of triangle is 1/2*b*8=8

Hence solving for b we get b=2. This point is (11,8). Hence E


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Re: In the figure above, a line segment joining the point (3,10) and which [#permalink]

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New post 18 Dec 2017, 03:57
First instinct is that there will be 2 such points - one lying on x = 11 and the other lying on y = 2.

Looking at the options, we see that we are looking for the point on x = 11. It will be much closer to (11, 10) than to (11, 2) so of the given options, (11, 8) makes the most sense. Let's check.

Area of square = 8*8 = 64

Area of right triangle made by (3, 10), (11, 8) and (11, 10) = (1/2)*2*8 = 8

This is 1/8th of the total area of the square and hence it satisfies our condition.

Answer (E)
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Re: In the figure above, a line segment joining the point (3,10) and which   [#permalink] 18 Dec 2017, 03:57
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In the figure above, a line segment joining the point (3,10) and which

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