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].
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].
