To solve the problem, we need to find the point on the [tex]\( y \)[/tex]-axis that is perpendicular to the given line passing through the point [tex]\((-2, 0)\)[/tex].
1. Identify the coordinates provided:
- The line passes through [tex]\((-3.6, 0)\)[/tex] and [tex]\((-2, 0)\)[/tex].
- We need to find the point on the [tex]\( y \)[/tex]-axis that is perpendicular to this line.
2. Understand the properties of the given points:
- Both points [tex]\((-3.6, 0)\)[/tex] and [tex]\((-2, 0)\)[/tex] lie on the [tex]\( x \)[/tex]-axis.
- A point on the [tex]\( y \)[/tex]-axis has coordinates in the form [tex]\((0, y)\)[/tex].
3. Determine the point on the [tex]\( y \)[/tex]-axis:
- Since the line is along the [tex]\( x \)[/tex]-axis, to find a point perpendicular on the [tex]\( y \)[/tex]-axis:
- The [tex]\( x \)[/tex]-coordinate of the point on the [tex]\( y \)[/tex]-axis will be [tex]\( 0 \)[/tex].
4. Identify the specific y-coordinate:
- The [tex]\( y \)[/tex]-coordinate of the point on the [tex]\( y \)[/tex]-axis will be the same as the [tex]\( x \)[/tex]-coordinate of the point [tex]\((-3.6, 0)\)[/tex] because we reflect the point along the line perpendicular to the [tex]\( x \)[/tex]-axis.
So, the coordinates of the point on the [tex]\( y \)[/tex]-axis perpendicular to the line passing through [tex]\((-2, 0)\)[/tex] will be [tex]\((0, -3.6)\)[/tex].
Hence, the required point on the [tex]\( y \)[/tex]-axis is [tex]\((0, -3.6)\)[/tex].
