Question

plot $(-3,6),(0,-5)$, and $(6,-2)$ in the $xy$-plane. tell in which quadrant or on what coordinate axis each point lies.
(a) choose the graph that correctly plots the point $(-3,6)$
in which quadrant does the point $(-3,6)$ lie?
quadrant iv
quadrant iii
quadrant ii
quadrant i
(b) choose the graph that correctly plots the point $(0,-5)$

Explanation:

Step1: Recall quadrant rules

In the \(xy -\)plane, quadrant I: \(x>0,y>0\); quadrant II: \(x < 0,y>0\); quadrant III: \(x<0,y < 0\); quadrant IV: \(x>0,y < 0\). For a point \((x,y)\), if \(x = 0\), the point lies on the \(y -\)axis; if \(y=0\), the point lies on the \(x -\)axis.

Step2: Analyze point \((-3,6)\)

For the point \((-3,6)\), \(x=-3<0\) and \(y = 6>0\). According to the quadrant rules, this point lies in quadrant II.

Step3: Analyze point \((0,-5)\)

For the point \((0,-5)\), \(x = 0\) and \(y=-5<0\). Since \(x = 0\), this point lies on the \(y -\)axis.

Step4: Analyze point \((6,-2)\)

For the point \((6,-2)\), \(x = 6>0\) and \(y=-2<0\). According to the quadrant rules, this point lies in quadrant IV.

Answer:

• The point \((-3,6)\) lies in quadrant II.
• The point \((0,-5)\) lies on the \(y -\)axis.
• The point \((6,-2)\) lies in quadrant IV.