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12 Sep 2018, 18:46
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WoundedTiger
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
27 Dec 2020, 22:11
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Point (a , b) can be any one of the following as examples:
(5 , 1) ---- Quadrant 1
(-5 , 1) ------- Quadrant 2
(-5, -1) --------Quadrant 3
(5 , -1) -------Quadrant 4
Which Point could be in the Same Quadrant as (a , b)? Given that (a , b) could be any of the 4 above
(A) (-b , -a)
if (a , b) = (5 , 1) ------- then (-1 , -5) ---NO
if (a , b) = (-5 , 1) -------then (-1 , 5) ---- YES
if (a , b) = (-5 , -1) -----then (1 , 5) ---- NO
if (a , b) = (5 , -1) -------then (1 , -5)------YES
If (a , b) is in Quadrant 4
then (-b , -a) will also be in Quadrant 4
or
If (a , b) is in Quadrant 2
then (-b , -a) will also be in Quadrant 2
(A)
(5 , 1) ---- Quadrant 1
(-5 , 1) ------- Quadrant 2
(-5, -1) --------Quadrant 3
(5 , -1) -------Quadrant 4
Which Point could be in the Same Quadrant as (a , b)? Given that (a , b) could be any of the 4 above
(A) (-b , -a)
if (a , b) = (5 , 1) ------- then (-1 , -5) ---NO
if (a , b) = (-5 , 1) -------then (-1 , 5) ---- YES
if (a , b) = (-5 , -1) -----then (1 , 5) ---- NO
if (a , b) = (5 , -1) -------then (1 , -5)------YES
If (a , b) is in Quadrant 4
then (-b , -a) will also be in Quadrant 4
or
If (a , b) is in Quadrant 2
then (-b , -a) will also be in Quadrant 2
(A)
14 Sep 2024, 01:52
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Another method using reflective properties.
I hope it is right.
reflection of (a,b)
over x-axis: a,-b
over y-axis: -a,b
origin: -a,-b
y=x: b,a
y=-x: -b,-a
A. (–b, –a)
this is over y=-x line. So could line in same quadrant.
B. (–a, –b)
this is over origin. So definitely not same quadrant.
C. (b, –a)
a,b when reflected over y=x becomes b,a. Still in same quadrant.
This is then reflected over x-axis then it becomes b,-a.
So in different quadrant.
D. (a, –b)
over axis reflected. Not in same quadrant.
E. (–b, a)
a,b when reflected over y=x becomes b,a. Still in same quadrant.
This is then reflected over y-axis then it becomes -b,a.
So in different quadrant.
I hope it is right.
reflection of (a,b)
over x-axis: a,-b
over y-axis: -a,b
origin: -a,-b
y=x: b,a
y=-x: -b,-a
A. (–b, –a)
this is over y=-x line. So could line in same quadrant.
B. (–a, –b)
this is over origin. So definitely not same quadrant.
C. (b, –a)
a,b when reflected over y=x becomes b,a. Still in same quadrant.
This is then reflected over x-axis then it becomes b,-a.
So in different quadrant.
D. (a, –b)
over axis reflected. Not in same quadrant.
E. (–b, a)
a,b when reflected over y=x becomes b,a. Still in same quadrant.
This is then reflected over y-axis then it becomes -b,a.
So in different quadrant.
