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Use the given line and the point not on the line to answer the question.

What is the point on the line perpendicular to the given line, passing through the given point, that is also on the [tex]y[/tex]-axis?

A. [tex](-3.6, 0)[/tex]
B. [tex](-2, 0)[/tex]
C. [tex](0, -3.6)[/tex]
D. [tex](0, -2)[/tex]

Sagot :

GinnyAnsweridn
To determine the point on the [tex]\( y \)[/tex]-axis which is closest to the point [tex]\((-3.6, 0)\)[/tex] and lies on a line perpendicular to the line passing through [tex]\((-3.6, 0)\)[/tex], we can proceed as follows:

1. Recognize that the point on the [tex]\( y \)[/tex]-axis we are looking for must have the [tex]\( x \)[/tex]-coordinate equal to 0, making it of the form [tex]\((0, y)\)[/tex].

2. The problem involves finding the perpendicular line from the given point [tex]\((-3.6, 0)\)[/tex] to the [tex]\( y \)[/tex]-axis. Perpendicular lines to the [tex]\( y \)[/tex]-axis are horizontal lines.

3. The horizontal line passing through the point [tex]\((-3.6, 0)\)[/tex] contains all points with the same [tex]\( y \)[/tex]-coordinate as [tex]\((-3.6, 0)\)[/tex], which is [tex]\( y = 0 \)[/tex].

4. The intersection of this horizontal line with the [tex]\( y \)[/tex]-axis occurs exactly at the origin [tex]\((0, 0)\)[/tex].

Therefore, the point on the [tex]\( y \)[/tex]-axis that is closest to the point [tex]\((-3.6, 0)\)[/tex] and lies on a line perpendicular to a vertical line passing through [tex]\((-3.6, 0)\)[/tex] is [tex]\((0, 0)\)[/tex].
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