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In the xy-coordinate plane there are 4 points A(2,0), B(4,0), C(4,2),

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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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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. \(\frac{1}{6}\)
[Reveal] Spoiler: OA

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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

Answer: Option 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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New post 16 Aug 2017, 02:42
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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] 16 Aug 2017, 02:42
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