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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 53% (02:29) correct 47% (02:32) wrong based on 78 sessions

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In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2), and D(2,2). If the line which passes through an origin bisects the area of the rectangle ABCD, what is the slope of the line?

A. $$\frac{1}{2}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{4}$$
D. $$\frac{1}{5}$$
E. $$\frac{1}{6}$$

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Re: In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),  [#permalink]

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MathRevolution wrote:
In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2), and D(2,2). If the line which passes through an origin bisects the area of the rectangle ABCD, what is the slope of the line?

A. $$\frac{1}{2}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{4}$$
D. $$\frac{1}{5}$$
E. $$\frac{1}{6}$$

A line can divide the area of rectangle into two equal parts only if it passes through the centre of quadrilateral as shown in figure...

Hence one of the points that the line will pass through will be midpoint of the diagonal [(2+4)/2 , (0+2)/2] = (3,1)

Another point that line is passing through is oriin i.e. (0,0)

hence slope = (1-0) / (3-0) = 1/3

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),  [#permalink]

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Attachment: 8.16.png [ 9.06 KiB | Viewed 914 times ]

The line should pass through the center (3,1) of the square ABCE. Thus its slope is 1/3.

Ans: B
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Re: In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),  [#permalink]

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_________________ Re: In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),   [#permalink] 15 Oct 2018, 07:00
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