To solve the problem of finding the point on the line perpendicular to the given line and passing through the given point [tex]\((-3.6, 0)\)[/tex], such that this point is also on the [tex]\(y\)[/tex]-axis, follow these steps:
1. Identify the characteristics of the point on the y-axis:
Any point that lies on the [tex]\(y\)[/tex]-axis has its [tex]\(x\)[/tex]-coordinate equal to 0. Therefore, we are looking for a point [tex]\((0, y)\)[/tex].
2. Understand the condition of perpendicularity:
A line perpendicular to another line will intersect at a right angle (90 degrees). In this context, we need a point that, when connected by a line to [tex]\((-3.6, 0)\)[/tex], forms a right angle with the given line's direction.
3. Identify the point given the conditions:
The problem gives us potential points to consider that lie on the [tex]\(y\)[/tex]-axis and maintains that we should analyze which fits a perpendicular condition.
Among the possible choices:
- [tex]\((-3.6, 0)\)[/tex]: This point does not lie on the [tex]\(y\)[/tex]-axis.
- [tex]\((-2, 0)\)[/tex]: This point does not lie on the [tex]\(y\)[/tex]-axis.
- [tex]\((0, -3.6)\)[/tex]: This point lies on the [tex]\(y\)[/tex]-axis.
- [tex]\((0, -2)\)[/tex]: This point also lies on the [tex]\(y\)[/tex]-axis.
Given the perpendicular condition and the potential points on the [tex]\(y\)[/tex]-axis, the point that connects perpendicularly with [tex]\((-3.6, 0)\)[/tex] taking into account the distances and orientations expected would logically be:
[tex]\((0, -3.6)\)[/tex]
Thus, the point on the [tex]\(y\)[/tex]-axis that is perpendicular to the given line and passing through [tex]\((-3.6, 0)\)[/tex] is:
[tex]\((0, -3.6)\)[/tex]
