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Coordinate Geometry - Help

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Coordinate Geometry - Help

by dqure040 » Wed Oct 14, 2015 6:24 pm
I do not understand the OG explanation to this problem, please help:

In the xy-plane, the points (c,d), (c, -d) & (-c, -d) are 3 vertices of a certain square. If c<0 and d>0, which of the following points is in the same quadrant as the fourth vertex of the square?
A.(-5,-3) B.(-5,3) C.(5,-3) D.(3,-5) or E.(3,5).

Answer is E, but I don't see why it isn't B based on the conditions for c & d.

Please and thank you!
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by Brent@GMATPrepNow » Wed Oct 14, 2015 6:49 pm
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points is in the same quadrant as the fourth vertex of the square?

A. (-5, -3)
B. (-5, 3)
C. (5, -3)
D. (3, -5)
E. (3, 5)
IMPORTANT: c < 0 and d > 0
In other words, c is NEGATIVE and d is POSITIVE

Let's examine each of the three given vertices:

(c, d): So, we get (NEGATIVE, POSITIVE). This vertex is in quadrant II
(c, -d): So, we get (NEGATIVE, -POSITIVE), which simplifies to (NEGATIVE, NEGATIVE). This vertex is in quadrant III
(-c, -d): So, we get (-NEGATIVE, -POSITIVE), which simplifies to (POSITIVE, NEGATIVE). This vertex is in quadrant IV

So, the last vertex must be in quadrant I
Only (3, 5) is in quadrant I

Answer: E

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Brent
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by [email protected] » Thu Oct 15, 2015 8:50 am
Hi dqure040,

You might find it helpful to TEST VALUES.

We're told that C < 0 and D > 0.

Let's TEST
C = -2
D = +2

We're given 3 of 4 co-ordinates for a square....
(C,D) = (-2, +2) which is in the 2nd Quadrant
(C, -D) = (-2, -2) which is in the 3rd Quadrant
(-C, -D) = (+2, -2) which is in the 4th Quadrant

Since we're dealing with a square, the 4th co-ordinate will be in 1st Quadrant...There's only one answer that's also in the 1st Quadrant...

Final Answer: E

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