Answered

Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.

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

Sagot :

GinnyAnsweridn
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
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.