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Plot each point in the [tex]\(xy\)[/tex]-plane. Tell in which quadrant or on what coordinate axis each point lies.

[tex]\[
\begin{array}{l}
A=(2,-6) \\
B=(-8,3) \\
C=(0,1)
\end{array}
\][/tex]
[tex]\[
D=(-3,-1)
\][/tex]
[tex]\[
E=(1,0)
\][/tex]

In which quadrant or on what axis does point [tex]\(A\)[/tex] lie?
A. Quadrant III
B. Quadrant IV
C. None, because the point is on the [tex]\(y\)[/tex]-axis
D. None, because the point is on the [tex]\(x\)[/tex]-axis
E. Quadrant I
F. Quadrant II

In which quadrant or on what axis does point [tex]\(B\)[/tex] lie?
A. None, because the point is on the [tex]\(y\)[/tex]-axis
B. Quadrant II
C. Quadrant I
D. Quadrant IV
E. None, because the point is on the [tex]\(x\)[/tex]-axis
F. Quadrant III



Answer :

GinnyAnswer
To determine the position of each point on the xy-plane, we start by plotting the given points:

1. [tex]\( A = (2, -6) \)[/tex]
2. [tex]\( B = (-8, 3) \)[/tex]
3. [tex]\( C = (0, 1) \)[/tex]
4. [tex]\( D = (-3, -1) \)[/tex]
5. [tex]\( E = (1, 0) \)[/tex]

We then determine which quadrant or axis each point lies in:

### Point A: [tex]\( (2, -6) \)[/tex]
- The x-coordinate is positive ([tex]\(2 > 0\)[/tex]), and the y-coordinate is negative ([tex]\(-6 < 0\)[/tex]).
- Points in this situation lie in Quadrant IV.

### Point B: [tex]\( (-8, 3) \)[/tex]
- The x-coordinate is negative ([tex]\(-8 < 0\)[/tex]), and the y-coordinate is positive ([tex]\(3 > 0\)[/tex]).
- Points in this situation lie in Quadrant II.

### Point C: [tex]\( (0, 1) \)[/tex]
- The x-coordinate is zero ([tex]\(0 = 0\)[/tex]), while the y-coordinate is positive ([tex]\(1 > 0\)[/tex]).
- Points with an x-coordinate of zero lie on the y-axis.

### Point D: [tex]\( (-3, -1) \)[/tex]
- The x-coordinate is negative ([tex]\(-3 < 0\)[/tex]), and the y-coordinate is negative ([tex]\(-1 < 0\)[/tex]).
- Points in this situation lie in Quadrant III.

### Point E: [tex]\( (1, 0) \)[/tex]
- The x-coordinate is positive ([tex]\(1 > 0\)[/tex]), while the y-coordinate is zero ([tex]\(0 = 0\)[/tex]).
- Points with a y-coordinate of zero lie on the x-axis.

Now, we address the specific questions:

#### In which quadrant or on what axis does point A lie?
- Point A lies in Quadrant IV.
- Thus, the answer is:
B. Quadrant IV

#### In which quadrant or on what axis does point B lie?
- Point B lies in Quadrant II.
- Thus, the answer is:
B. Quadrant II

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