To determine which of the given ordered pairs represents a point located on the [tex]$y$[/tex]-axis, we need to understand the concept of the [tex]$y$[/tex]-axis in a coordinate plane. The [tex]$y$[/tex]-axis consists of all points where the [tex]$x$[/tex]-coordinate is zero.
Let's analyze each of the ordered pairs to see if the [tex]$x$[/tex]-coordinate is zero:
a. [tex]\((0, 3)\)[/tex]
- Here, the [tex]$x$[/tex]-coordinate is [tex]\(0\)[/tex]. Thus, this point lies on the [tex]$y$[/tex]-axis.
b. [tex]\((4, -4)\)[/tex]
- In this pair, the [tex]$x$[/tex]-coordinate is [tex]\(4\)[/tex]. Since it is not zero, this point does not lie on the [tex]$y$[/tex]-axis.
c. [tex]\((1, 1)\)[/tex]
- In this pair, the [tex]$x$[/tex]-coordinate is [tex]\(1\)[/tex]. Since it is not zero, this point does not lie on the [tex]$y$[/tex]-axis.
d. [tex]\((-2, 0)\)[/tex]
- Here, the [tex]$x$[/tex]-coordinate is [tex]\(-2\)[/tex]. Since it is not zero, this point does not lie on the [tex]$y$[/tex]-axis.
From this analysis, we can see that the only pair in which the [tex]$x$[/tex]-coordinate is zero is [tex]\((0, 3)\)[/tex]. Therefore, the ordered pair that is represented by a point located on the [tex]$y$[/tex]-axis is:
a. [tex]\((0, 3)\)[/tex]
So, the correct answer is:
a. [tex]$(0, 3)$[/tex]
