Normal Line Calculator

The Normal Line Calculator computes the equation and slope of the normal line at a given point on an original line, including the angle it forms with the original line, based on the point’s coordinates and the original line’s slope.

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How to Use the Normal Line Calculator

To effectively use the Normal Line Calculator, follow these step-by-step instructions. This guide will help ensure that you input the correct data and understand the results provided by the calculator.

Step 1: Enter the Coordinates of the Point

Start by entering the x-coordinate and y-coordinate of the point through which the normal line passes. These fields are labeled as Point x₁ and Point y₁, respectively.

  • Locate the Point x₁ input field. Here, type the x-coordinate of your point. Ensure the value is accurate to two decimal places using a step of 0.01.
  • In the Point y₁ input field, enter the y-coordinate of the point. Similar to the x-coordinate, maintain a precision of two decimal places with a step of 0.01.

Step 2: Enter the Slope of the Original Line

Next, input the slope of the original line using the field labeled Slope of Original Line (m). This will allow the calculator to determine the slope of the normal line.

  • Type the slope value into the input field. Make sure to use a precision of up to two decimal places, with a step increment of 0.01.

Step 3: Understand the Results

Once you have entered the required values, the calculator will compute various results relating to the normal line.

  • Normal Line Slope: The calculator provides the slope of the normal line using the formula -1 / slope. This value is displayed with four decimal places.
  • Normal Line Y-Intercept: The y-intercept of the normal line is calculated and displayed. The formula used is y1 - ((-1 / slope) * x1), also shown to four decimal places.
  • Normal Line Equation: The resulting equation of the normal line is presented in the format y = mx + b, where m and b are replaced by the computed slope and y-intercept, respectively.
  • Angle with Original Line (degrees): Finally, the calculator provides the angle between the original line and the normal line in degrees, calculated using the formula abs(atan((-1/slope - slope)/(1 + (-1/slope * slope)))) * (180/pi). The angle is presented with two decimal places and is appended with a degree symbol (°).

By carefully following these steps, you can utilize the Normal Line Calculator to accurately determine the characteristics of the normal line relative to the original line through the specified point.