Question

name the quadrant or axis where each point lies.
point a
the x - coordinate is negative and the y - coordinate is zero.
location: (choose one)
point b
the x - coordinate is positive and the y - coordinate is negative.
location: (choose one)

Explanation:

for Point A:

Step1: Recall axis/quadrant rules

For a point \((x,y)\), if \(y = 0\) and \(x
eq0\), it's on the \(x\)-axis. If \(x<0\) and \(y = 0\), it's on the negative \(x\)-axis.

Step2: Analyze Point A's coordinates

Point A has \(x\)-coordinate negative (\(x<0\)) and \(y\)-coordinate zero (\(y = 0\)). So it lies on the \(x\)-axis (specifically the negative \(x\)-axis).

for Point B:

Step1: Recall quadrant rules

Quadrants are defined by \(x\) and \(y\) signs:

• Quadrant I: \(x>0,y>0\)
• Quadrant II: \(x<0,y>0\)
• Quadrant III: \(x<0,y<0\)
• Quadrant IV: \(x>0,y<0\)

Step2: Analyze Point B's coordinates

Point B has \(x\)-coordinate positive (\(x>0\)) and \(y\)-coordinate negative (\(y<0\)). So it lies in Quadrant IV.

Answer:

• Point A Location: Negative \(x\)-axis (or \(x\)-axis, since \(y = 0\) and \(x<0\))
• Point B Location: Quadrant IV