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Plot each point in the xy-plane. Identify the quadrant or coordinate axis where each point lies.

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

In which quadrant or on what axis does point A lie?

A. Quadrant III
B. Quadrant IV
C. None, because the point is on the y-axis
D. None, because the point is on the x-axis
E. Quadrant I
F. Quadrant II

Sagot :

GinnyAnsweridn
To determine in which quadrant or on what axis the given points lie, we need to examine the coordinates of each point and then classify them based on their x and y values. Let's break this down step by step.

1. Point A = (2, -6)
- x-coordinate: 2 (positive)
- y-coordinate: -6 (negative)
- Since the x-coordinate is positive and the y-coordinate is negative, Point A lies in Quadrant IV.

2. Point B = (-8, 3)
- x-coordinate: -8 (negative)
- y-coordinate: 3 (positive)
- Since the x-coordinate is negative and the y-coordinate is positive, Point B lies in Quadrant II.

3. Point C = (0, 1)
- x-coordinate: 0
- y-coordinate: 1 (positive)
- Since the x-coordinate is 0 and the y-coordinate is non-zero, Point C lies on the y-axis.

4. Point D = (-3, -1)
- x-coordinate: -3 (negative)
- y-coordinate: -1 (negative)
- Since both the x-coordinate and y-coordinate are negative, Point D lies in Quadrant III.

5. Point E = (1, 0)
- x-coordinate: 1 (positive)
- y-coordinate: 0
- Since the y-coordinate is 0 and the x-coordinate is non-zero, Point E lies on the x-axis.

Now, the question specifically asks about Point A. Based on our analysis, Point A has the coordinates (2, -6), placing it in Quadrant IV.

Therefore, the correct answer is:

B. Quadrant IV.
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