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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]  15 Apr 2018, 08:31
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78% (02:04) correct 21% (01:28) wrong based on 56 sessions

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#GREpracticequestion In the rectangular coordinate system shown.jpg [ 23.58 KiB | Viewed 574 times ]

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]  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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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: In the rectangular coordinate system shown, points A and E [#permalink]  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]  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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