Question

name the quadrant or axis where each point lies.
(7, -6): (choose one)
(-7, 0): (choose one)
(7, 3): (choose one)
(-3, 3): (choose one)

Explanation:

Step1: Recall quadrant rules

In a Cartesian - coordinate system, if \(x>0\) and \(y < 0\), the point is in the fourth quadrant; if \(x<0\) and \(y = 0\), the point is on the \(x\) - axis; if \(x>0\) and \(y>0\), the point is in the first quadrant; if \(x<0\) and \(y>0\), the point is in the second quadrant.

Step2: Analyze point \((7,-6)\)

Here \(x = 7>0\) and \(y=-6 < 0\), so it is in the fourth quadrant.

Step3: Analyze point \((-7,0)\)

Since \(y = 0\) and \(x=-7<0\), it lies on the negative \(x\) - axis.

Step4: Analyze point \((7,3)\)

As \(x = 7>0\) and \(y = 3>0\), it is in the first quadrant.

Step5: Analyze point \((-3,3)\)

Because \(x=-3<0\) and \(y = 3>0\), it is in the second quadrant.

Answer:

\((7,-6)\): Fourth quadrant
\((-7,0)\): Negative \(x\) - axis
\((7,3)\): First quadrant
\((-3,3)\): Second quadrant