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Which of the following points could lie in the same quadrant

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Which of the following points could lie in the same quadrant

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Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (-b, -a)
B. (-a, -b)
C. (b, -a)
D. (a, -b)
E. (-b, a)

OA A

Source: Manhattan Prep

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BTGmoderatorDC wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (-b, -a)
B. (-a, -b)
C. (b, -a)
D. (a, -b)
E. (-b, a)

OA A

Source: Manhattan Prep
Hello BTGmoderatorDC,

Pl. first search a question and then post. This question is already asked and replied last month. Pl. find it here.

https://www.beatthegmat.com/which-of-the-following-points-could-lie-in-the-same-quadrant-t303855.html#818626

Hope this helps!

-Jay
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BTGmoderatorDC wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (-b, -a)
B. (-a, -b)
C. (b, -a)
D. (a, -b)
E. (-b, a)
Let's test some coordinates...

How about: a = 1 and b = -2.
This means the point (a, b) = (1, -2), which is in QUADRANT IV

Now plug a = 1 and b = -2 into each answer choice...

A) (-b, -a) = [( -(-2), -1] = (2, -1), which is also in QUADRANT IV
PERFECT!

Answer: A

Cheers,
Brent

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Post
BTGmoderatorDC wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (-b, -a)
B. (-a, -b)
C. (b, -a)
D. (a, -b)
E. (-b, a)

Source: Manhattan Prep
Just a quick observation that is (I hope) interesting in its own right:

If x*y and w*z are both different from zero, points (x,y) and (w,z) will be in the same quadrant if, and only if,
x*w> 0 ("x-coordinates" have the same sign) and y*z>0 ("y-coordinates" have the same sign).

Conclusion:

(B) is refuted, because a and -a (x-coordinates in question stem and in this alternative choice) do not have the same signs (a is not zero)
(C) is refuted, because if a and b (x-coordinates...) have the same signs , then b and -a (y-coordinates...) don´t have
(D) is refuted, because b and -b (y-coordinates...) do not have the same signs (b is not zero)
(E) is refuted, because if a and -b (x-coordinates...) have the same signs , then b and a (y-coordinates...) don´t have

Regards,
fskilnik.

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BTGmoderatorDC wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (-b, -a)
B. (-a, -b)
C. (b, -a)
D. (a, -b)
E. (-b, a)
Let’s suppose that (a, b) lies in Quadrant IV. That is, a is positive and b is negative.

Thus, -b is positive and -a is negative, so (-b, -a) also lies in Quadrant IV.

Alternate Solution:

If we assume that both a and b are positive, and thus (a, b) is in Quadrant I, we see that none of the answer choices will lie in Quadrant I.

Now let’s assume that a is positive (a = 1) and b is negative (b = -2); then (1, -2) lies in Quadrant IV. Looking at the answer choices, we see that choice A gives us (-b, -a) =(2, -1), which is also in Quadrant IV.

Answer: A

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