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In the rectangular coordinate system shown, points A and E

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In the rectangular coordinate system shown, points A and E [#permalink] New post 15 Apr 2018, 08:31
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In the rectangular coordinate system shown, points A and E lie on the x-axis, and points B and D lie on the y-axis. Point C is the midpoint of the line AB, and point F is the midpoint of the line DE.

Quantity A
Quantity B
The slope of the line AB
The slope of the line DE


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Re: In the rectangular coordinate system shown, points A and E [#permalink] New post 23 Apr 2018, 01:50
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In the line \(AB\) by visualization point \(A\) is \((x,0)\).
and point \(B\) is \((0,y)\)

Since the given point \(c(-3,5)\) is the mid-point of the line we can make a eqn
\(x + 0/2 = -3\)
or, \(x = -6\)

\(\frac{y + 0}{2} = 5\)
therefore \(y = 10\)
For line \(AB\) \(A(-6,0) B(0,10)\)
Now, we can similarly calculate the value of point \(D\) and \(E\) in the line \(DE\)
Point \(D(0,y)\) and point \(E(x,0)\)
Hence, \(\frac{0+x}{2} = 3 or x = 6\)
\(\frac{y+0}{2} = -5\)
or, \(y=-10\)
For line \(DE\) D(0,-10) and \(E(6,0)\)

when we have two points we can calculate the slope for each line AB and DE we have three set of points so we can calculate slope
For the line \(AB\) slope \(= \frac{10-0}{0-(-6)} = \frac{10}{6} = \frac{5}{3}\)
For the line \(DE\) slope \(= \frac{0-(-10)}{6-0} = \frac{5}{3}\)
option c
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Re: In the rectangular coordinate system shown, points A and E [#permalink] New post 10 Sep 2018, 10:20
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not going into too much mathematical details:


points C & F are midpoints

both the lines are increasing

so they are parallel and hence they have th same positive slopes: 5/3.
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Re: In the rectangular coordinate system shown, points A and E [#permalink] New post 11 Sep 2018, 11:09
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Instead of finding the slopes ,easier way would be to see the symmetry in the figure.

You can observe both the lines are parallel.

So ans is C :)
Re: In the rectangular coordinate system shown, points A and E   [#permalink] 11 Sep 2018, 11:09
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