Question

identify the location of each of the points plotted on the coordinate plane below: on the x - axis, on the y - axis, in quadrant i, in quadrant ii, in quadrant iii, in quadrant iv, on the origin
9.
a
b
c
d
e
f
g
h
10.
a
b
c
d
e
f
g
h

Explanation:

Step1: Determine quadrant rules

Quadrant I: \(x>0,y>0\); Quadrant II: \(x < 0,y>0\); Quadrant III: \(x<0,y < 0\); Quadrant IV: \(x>0,y < 0\); \(x -\)axis: \(y = 0\); \(y -\)axis: \(x=0\); origin: \((0,0)\)

Step2: Analyze point A in first coordinate - plane

For point \(A\) in the first coordinate - plane: \(x = 0\) (since it lies on the \(y -\)axis), so \(A\) is on the \(y -\)axis.

Step3: Analyze point B in first coordinate - plane

For point \(B\): \(x>0,y>0\), so \(B\) is in Quadrant I.

Step4: Analyze point C in first coordinate - plane

For point \(C\): \(x>0,y < 0\), so \(C\) is in Quadrant IV.

Step5: Analyze point D in first coordinate - plane

For point \(D\): \(x<0,y>0\), so \(D\) is in Quadrant II.

Step6: Analyze point E in first coordinate - plane

For point \(E\): \(x<0,y = 0\) (since it lies on the \(x -\)axis), so \(E\) is on the \(x -\)axis.

Step7: Analyze point F in first coordinate - plane

For point \(F\): \(x = 0,y<0\) (since it lies on the \(y -\)axis), so \(F\) is on the \(y -\)axis.

Step8: Analyze point G in first coordinate - plane

For point \(G\): \(x<0,y < 0\), so \(G\) is in Quadrant III.

Step9: Analyze point H in first coordinate - plane

For point \(H\): \(x = 0,y = 0\), so \(H\) is the origin.

Step10: Analyze point A in second coordinate - plane

For point \(A\) in the second coordinate - plane: \(x<0,y = 0\) (since it lies on the \(x -\)axis), so \(A\) is on the \(x -\)axis.

Step11: Analyze point B in second coordinate - plane

For point \(B\): \(x<0,y>0\), so \(B\) is in Quadrant II.

Step12: Analyze point C in second coordinate - plane

For point \(C\): \(x>0,y>0\), so \(C\) is in Quadrant I.

Step13: Analyze point D in second coordinate - plane

For point \(D\): \(x = 0,y<0\) (since it lies on the \(y -\)axis), so \(D\) is on the \(y -\)axis.

Step14: Analyze point E in second coordinate - plane

For point \(E\): \(x>0,y < 0\), so \(E\) is in Quadrant IV.

Step15: Analyze point F in second coordinate - plane

For point \(F\): \(x<0,y<0\), so \(F\) is in Quadrant III.

Step16: Analyze point G in second coordinate - plane

For point \(G\): \(x>0,y>0\), so \(G\) is in Quadrant I.

Step17: Analyze point H in second coordinate - plane

For point \(H\): \(x = 0,y = 0\), so \(H\) is the origin.

Answer:

9.
A: on the \(y -\)axis
B: in Quadrant I
C: in Quadrant IV
D: in Quadrant II
E: on the \(x -\)axis
F: on the \(y -\)axis
G: in Quadrant III
H: origin
10.
A: on the \(x -\)axis
B: in Quadrant II
C: in Quadrant I
D: on the \(y -\)axis
E: in Quadrant IV
F: in Quadrant III
G: in Quadrant I
H: origin