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!
Coordinate Geometry - Help
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IMPORTANT: c < 0 and d > 0In 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)
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
Cheers,
Brent
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich