Answered

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]



Answer :

To solve the problem of finding the points on the \(y\)-axis that lie on a line perpendicular to a given horizontal line and pass through given points, we need to follow these steps:

1. Identify the Given Information:
- The points given are \((-3.6, 0)\), \((-2, 0)\), \((0, -3.6)\), and \((0, -2)\).
- The \((x, y)\)-coordinates of these points provide the positions relative to the origin.

2. Understand the Characteristics of the Lines:
- The given points \((-3.6, 0)\) and \((-2, 0)\) lie on a horizontal line (y=0), which implies the slope of this line is 0.
- A line perpendicular to a horizontal line has an undefined slope, meaning it is a vertical line.

3. Identify the Perpendicular Line:
- Vertical lines parallel to the \(y\)-axis take the general form \(x = k\), where \(k\) is a constant. Therefore, any vertical line will intersect the \(y\)-axis at any value of y.

4. Identify Points on the \(y\)-axis:
- From the given points, \((0, -3.6)\) and \((0, -2)\) are on the \(y\)-axis because their \(x\)-coordinates are zero. These points lie directly on the vertical line \(x = 0\).

5. Conclusion:
- The points \((0, -3.6)\) and \((0, -2)\) on the \(y\)-axis are the required points that lie on a line perpendicular to the given horizontal line and pass through the given points.

Thus, the points on the [tex]\(y\)[/tex]-axis that are also on the line perpendicular to the given horizontal line passing through the given points are [tex]\((0, -3.6)\)[/tex] and [tex]\((0, -2)\)[/tex].