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)
How will i start the solution in this problem?
OA A
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Which of the following points
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Every answer choice includes at least one negative sign.Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠0 ?
(-b, -a)
(-a, -b)
(b, -a)
(a, -b)
(-b, a)
Test coordinate pairs that include at least one negative value.
Case 1: a=1 and b=-1, so that (a, b) = (1, -1)
Plug a=1 and b=-1 into the answer choices to see whether one of the answer choices yields a point in the same quadrant as (1,-1).
A: (-b, -a) = ( -(-1), -1 ) = (1, -1).
Success!
The correct answer is A.
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Let's suppose that (a, b) lies in Quadrant IV. That is, a is positive and b is negative.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)
How will i start the solution in this problem?
OA A
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, then (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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