Our Perpendicular Line Calculator is a fantastic tool if you need to answer a geometry problem fast. Trust us! It determines the equation of a (yet undefined) line perpendicular to a given line and passing through a specified point. It also determines the coordinates of the location where the two lines meet. So enter the coordinates of any point and the coefficients characterizing the supplied line into our perpendicular line equation calculator, and we’ll do the rest!

If you are interested in this calculator, or similar to this, be sure to check out other related calculators, such as Pythagorean Theorem, Parallel Line Calculator or this Multiplying Radicals Calculator.

Perpendicular Lines

A perpendicular is a straight line that intersects another line at a 90° angle. As seen in the diagram, 90° is a right angle and is shown by a little square between two perpendicular lines. Two lines that meet at a 90-degree angle are called perpendicular. Have you seen anything similar to the letter “L” or the connecting corners of your walls? They are perpendicular lines, which are straight lines that meet at a specified angle – the right angle.

Perpendicular Line

Perpendicular lines have two basic characteristics:

  • they always meet or intersect with one other,
  • any angle formed by two perpendicular lines is always 90 degrees.

We need a scale (ruler), a compass, or a protractor to draw a perpendicular line with any point. We’ll go through how to draw the perpendicular line with a compass and a protractor step by step. So there are two ways to draw perpendicular lines for a given line:

  • making use of a protractor,
  • making use of a compass.

Parallel and Perpendicular Lines

Parallel and perpendicular lines are significant in geometry, and they have distinguishing properties that make them easy to distinguish. For example, if two lines lay in the same plane, are the same distance apart, and never intersect, they are said to be parallel.

Parallel lines are two straight lines in the same plane that never meet. They are central lines because they are always the same distance apart. Parallel lines are represented by the symbol ||.

Here is the table so you can better understand it, and directly see the difference:

Parallel Perpendicular
Lines that do not cross and are always the same distance apart are called parallel lines.Perpendicular lines are those that make a straight angle when they intersect.
A straight ladder’s steps are an example, as are the opposing sides of a rectangle.  For instance, at the intersection of two walls, the letter “L.”  
The symbol || is used to represent two parallel lines.  Two perpendicular lines are represented by the symbol ⊥.  
Table with the main differences between parallel and perpendicular lines

Perpendicular Lines Equation

The perpendicular lines formula is used to determine whether or not two provided lines are perpendicular. When we know the slope of two lines we wish to compare, we may use the perpendicular line’s formula. This is a very useful form.

A basic line equation may be used to describe any straight line in a two-dimensional space:

y=  {ax + b} 

a and b  coefficients, 

x – x coordinate, and 

y – y coordinate

Let’s assume that the provided line’s equation is: 

y=  {mx + r} 

You know what m and r are and want to find a line perpendicular to this one. You also know the coordinates of the spot through which your line should travel. They are x0 and y0, respectively. The value of a coefficient equals the slope of any line. The product of the slopes of two perpendicular lines equals point -1.

It would help if you replaced the coordinates or point (x0, y0) and the value of an into the equation of your line to determine the b coefficient (also known as the y-intercept).

y=  {mx + r} 
y_0= \frac {-1 \times x_0 }{m + b}
b= \frac {y_0 +1\times x_0 }{m}

Perpendicular Line Calculator – How to Use?

So we already mentioned that this is an amazing tool. You may use this calculator to compute the equation of a perpendicular line. To use the calculator, follow the instructions below:

  1. Enter in the values for the line equation and coordinates in the appropriate input boxes.
  2. To acquire the perpendicular line equation, click “Calculate.” And you get the whole form.
  3. To clear the fields and enter new values, click “Reset.”

This calculator is amazing, isn’t it, you get the point!

Perpendicular Line Calculator – Example

We have the next details, so you need to find the equation of the line that is perpendicular to the line given:

3y – x = 6.

And the points that we will take are (4,2).

Step 1 – enter in the formula

y = mx + b

3y – x = 6

3y = 6 + x

y = (6/3) + (x/3)

y = 2 + (x/3) or y = ((1/3) × x) + 2

m = 1/3

Step 2

Negative reciprocal value of slope is m = -3

Step 3

The perpendicular line with a slope of -3 goes through the coordinates (4,2). As a result, the equation is 2 = ((-3) 4) + b. We obtain b = 14 after solving the problem in the form.

Step 4

The perpendicular line’s equation is y = -3x +14.

Now use the calculator to calculate the perpendicular line equations.

5x + 6y = 10, which is the result of traveling through the coordinates (2,3).

2x + y = 4, traversing the given coordinates (1,2).

Perpendicular lines in Real Life

We went through basic geometry in smaller groups, where perpendicular lines refer to the relationship between any kind of two lines that are going to meet at a point and form a right angle to each other.

Perpendicular lines have several interesting facts:

  • At right angles, this line always meets.
  • Two parallel lines that are perpendicular to each other will never intersect.
  • We can’t argue that intersecting lines are always perpendicular since we can’t say that perpendicular lines are always intersecting.
  • The following are instances of perpendicular lines in real life:
  • On the football pitch,
  • Crossing a railway track,
  • Kit for first aid,
  • The construction form of a home with perpendicular floors and walls, and
  • Window designs for televisions.

At their junction point, perpendicular lines generate four right angles, totaling 360 degrees. Perpendicular lines also make up one of the right triangle’s angles. When students learn to compute the slopes of lines on graph paper, they are taught about perpendicular lines in algebra and geometry.

FAQ

How to find a perpendicular line?

The slope of the line we wish to calculate is 1/2 because perpendicular lines have opposite reciprocal slopes.

How do you know if an equation is perpendicular to a line?

We can say that if any slopes of two lines can be computed, multiplying their slopes is a simple technique to see if they are perpendicular. The lines are perpendicular if the product of the slopes is equal.

Do perpendicular lines have the same slope?

Perpendicular lines have different slopes. The slopes of perpendicular lines differ in a certain way from one another. The slope of one line is the negative reciprocal of the slope of the other line.

Do perpendicular lines intersect?

Lines that cross at a 90-degree angle are known as perpendicular lines.

How do you write an equation of a line perpendicular to y = −2x + 5 and passes through the given point (1,4)?

A line perpendicular to a line with the equation y = 2x + 5 has a slope of – 1/2.

Does a square have perpendicular lines?

Squares have four pairs of perpendicular lines.