MATH CALCULATOR
Perpendicular Line Calculator
Calculate the equation of a line perpendicular to another given its slope and a point it passes through.
What is the Perpendicular Line Calculator & How does it work?
Two lines are perpendicular if the product of their slopes is -1. If you have a line with slope m, any line perpendicular to it will have a slope of -1/m.
To find the equation of a perpendicular line passing through a point (x1, y1), use the point-slope form: y – y1 = mperp(x – x1).
m_perp = -frac{1}{m}
m_perp = slope of the perpendicular line
m = slope of the original line
m = slope of the original line
To find the equation of a perpendicular line passing through a point (x1, y1), use the point-slope form: y – y1 = mperp(x – x1).
Parameters
Equation of Perpendicular Line—
Frequently Asked Questions
How do I find the slope of a line that is perpendicular to another?
To find the slope of a line that is perpendicular to another, take the negative reciprocal of the original line’s slope. If the original line has a slope of m, the perpendicular line’s slope will be -1/m.
Can you explain how to use the point-slope form to find the equation of a perpendicular line?
Yes, using the point-slope form y – y1 = m(x – x1), where (x1, y1) is a point on the perpendicular line and m is its slope. Substitute the slope of the perpendicular line and the coordinates of the point into the formula to get the equation.
What if I only have one point and need to find the equation of a line perpendicular to another line?
First, determine the slope of the given line. Then, find the negative reciprocal of that slope for the perpendicular line. Use the point-slope form with your point and the new slope to find the equation.
How do I check if two lines are perpendicular?
Multiply the slopes of the two lines. If the product is -1, the lines are perpendicular.
Can you give an example of finding a perpendicular line’s equation?
Sure! If you have a line with a slope of 2 and it passes through (3, 4), the perpendicular line has a slope of -1/2. Using the point-slope form: y – 4 = (-1/2)(x – 3). Simplify to get the equation.
What happens if the original line is horizontal or vertical?
If the original line is horizontal (slope = 0), the perpendicular line will be vertical (undefined slope). If it’s vertical, the perpendicular line will be horizontal (slope = 0).
How do I find the equation of a perpendicular bisector?
To find the equation of a perpendicular bisector, first find the midpoint of the segment and calculate the slope of the original line. The perpendicular bisector’s slope will be the negative reciprocal of the original line’s slope. Use the point-slope form with the midpoint as the point.
Results are for informational purposes only and do not constitute professional advice.