To determine which quadrant the points with [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex] reside in, we recall the definitions for the coordinate plane:
1. The first quadrant contains points where both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are positive: [tex]\(x > 0\)[/tex] and [tex]\(y > 0\)[/tex].
2. The second quadrant contains points where [tex]\(x\)[/tex] is negative and [tex]\(y\)[/tex] is positive: [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex].
3. The third quadrant contains points where both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are negative: [tex]\(x < 0\)[/tex] and [tex]\(y < 0\)[/tex].
4. The fourth quadrant contains points where [tex]\(x\)[/tex] is positive and [tex]\(y\)[/tex] is negative: [tex]\(x > 0\)[/tex] and [tex]\(y < 0\)[/tex].
Given the specific conditions [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex], this configuration corresponds to the second quadrant.
Thus, all the points which have [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex] are existing in the second quadrant.
