To determine the point on the line perpendicular to the given line and passing through the given point on the [tex]\(y\)[/tex]-axis, we follow these steps:
1. Understanding the Given Line:
- The points on the given line are [tex]\((-3.6, 0)\)[/tex] and [tex]\((-2, 0)\)[/tex].
- Since both points have the same [tex]\(y\)[/tex]-coordinate (which is 0), the line is horizontal.
2. Perpendicularity:
- A line perpendicular to a horizontal line is a vertical line. This means that the [tex]\(x\)[/tex]-coordinate of the point where the perpendicular line intersects the [tex]\(y\)[/tex]-axis will be consistent with the x-coordinate of the given point on the x-axis.
3. Identifying the Perpendicular Line:
- Since the [tex]\(y\)[/tex]-axis is vertical, any line perpendicular to the horizontal line must intersect the [tex]\(y\)[/tex]-axis at [tex]\(x = 0\)[/tex].
4. Point on the y-axis:
- We need to find a point on the y-axis that makes the line perpendicular to the given horizontal line and lies on the [tex]\(y\)[/tex]-axis.
Given the options for possible points on the [tex]\(y\)[/tex]-axis:
[tex]\[ (0, -3.6) \][/tex]
[tex]\[ (0, -2) \][/tex]
5. Checking the Conditions:
- The point directly fulfills the perpendicularity condition since our horizontal line differs precisely by moving up or down [tex]\(0.0\)[/tex].
- Among the given points on the [tex]\(y\)[/tex]-axis:
- [tex]\(y\)[/tex]-coordinates [tex]\((-3.6, -2)\)[/tex]
Therefore, the correct point that lies on the y-axis and forms a line perpendicular to the given horizontal line is:
[tex]\[
\boxed{(0, -2)}
\][/tex]
