Write the Equation of a Line Perpendicular Calculator
Calculating the equation of a line perpendicular to a given line is a fundamental concept in mathematics, particularly in geometry and trigonometry. This skill is crucial in various fields, including engineering, architecture, and data analysis.
- Enter the x and y coordinates of a point on the given line.
- Enter the slope of the given line.
- Click ‘Calculate’ to find the equation of the perpendicular line.
The slope of a line perpendicular to another is the negative reciprocal of the original slope. The formula to find the slope (m’) of the perpendicular line is:
m’ = -1 / m
Using the point-slope form of a linear equation (y – y1 = m'(x – x1)), we can find the equation of the perpendicular line.
| Given Line Slope (m) | Perpendicular Line Slope (m’) |
|---|---|
| 2 | -0.5 |
| -3 | 0.333 |
| 0 | undefined |
| Given Line Equation (y – y1 = m(x – x1)) | Perpendicular Line Equation (y – y1 = m'(x – x1)) |
|---|---|
| y – 3 = 2(x – 1) | y – 3 = -0.5(x – 1) |
| y + 2 = -3(x + 4) | y + 2 = 0.333(x + 4) |
| y = 5 | Not applicable (horizontal line) |
- Remember, two lines are perpendicular if the product of their slopes is -1.
- If the given line is vertical (undefined slope), the perpendicular line will be horizontal (slope = 0).
What if the given line is horizontal?
If the given line is horizontal (slope = 0), the perpendicular line will be vertical (undefined slope).
Can I find the equation of a line parallel to a given line?
Yes, the slope of a line parallel to another is the same. So, the slope of the parallel line (m’) is equal to the slope of the given line (m).