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Which of the following sets of ordered pairs lie on the [tex]$y$[/tex]-axis of a coordinate grid?

A. [tex]$(3, -1)$[/tex]
B. [tex]$(0, -4)$[/tex]
C. [tex]$(-3, 0)$[/tex]
D. [tex]$(-4, 0)$[/tex]

Sagot :

GinnyAnsweridn
To determine which of the given sets of ordered pairs lie on the [tex]\( y \)[/tex]-axis of a coordinate grid, we need to consider the definition of the [tex]\( y \)[/tex]-axis. Specifically, a point lies on the [tex]\( y \)[/tex]-axis if and only if its [tex]\( x \)[/tex]-coordinate is zero.

Let's analyze each given ordered pair:

1. [tex]\((3, -1)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is 3.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.

2. [tex]\((0, -4)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is 0.
- Since the [tex]\( x \)[/tex]-coordinate is zero, this point lies on the [tex]\( y \)[/tex]-axis.

3. [tex]\((-3, 0)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is -3.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.

4. [tex]\((-4, 0)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is -4.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.

After analyzing each pair, we conclude that the only pair that lies on the [tex]\( y \)[/tex]-axis is [tex]\((0, -4)\)[/tex].
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