If a and b are nonzero, does the point (a,b) lie in the quadrant II of

If a and b are nonzero, does the point (a,b) lie in the quadrant II of the xy plane?


(1) a = -b

(2) a < 0

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Solution

Step 1: Analyse Question Stem

• \(a ≠ 0\)
• \(b≠ 0\)

• So, if we know the sign of a and b we can decide whether point(a,b) lies in quadrant II or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• Per this statement, we can say that a and b have opposite signs. So

o Case I: If \(b > 0\) then \(a < 0 \)

 Hence, point (a, b) lies in II quadrant.
o Case II: If \(b < 0 \)then \(a > 0 \)

 Hence, point (a, b) lies in IV quadrant.

• We don’t know about b. So,

o Case I: If \(b > 0\) then point (a,b) lies in II quadrant.
o Case II: If \(b < 0\), then point(a,b) lies in III quadrant.

Step 3: Analyse Statements by combining.

• From statement 1:

o If \(b > 0 \) then \(a < 0\)
o And , if \(b < 0\) then \(a > 0\)
• From statement 2: \(a < 0\)
• On combining both statements, we get,

o \(a < 0\) and \(b > 0\)
o Therefore, point (a, b) lies in II quadrant.