Distance Between a Point and a Line In 2D & 3D - Geometry

TL;DR

Learn how to find the perpendicular distance between a point and a line in both two and three dimensions.

Transcript

in this video we're going to focus on calculating the distance between a point and a line in two dimensions and in three dimensions so let's say if we have a graph and this is just some generic equation so let's say this is a line and the formula is ax plus b y plus c is equal to zero and we have some point x comma y the distance formula will give ... Read More

Key Insights

• 🫥 The distance between a point and a line in both two and three dimensions can be calculated using a standard formula.
• 🫥 The formula involves determining the coefficients of the line equation and substituting them along with the coordinates of the point.
• 🫥 The absolute value ensures a positive distance, representing the perpendicular distance between the point and the line.

Questions & Answers

Q: What is the formula to calculate the distance between a point and a line in two dimensions?

The formula is d = |ax1 + by1 + c| / √(a^2 + b^2), where (x1, y1) represents the coordinates of the point and a, b, and c are the coefficients of the line equation.

Q: How do you calculate the distance in three dimensions?

For three dimensions, the formula is d = |ax1 + by1 + cz1 + d| / √(a^2 + b^2 + c^2), where (x1, y1, z1) represents the coordinates of the point and a, b, c, and d are the coefficients of the line equation.

Q: What does the absolute value signify in the distance formula?

The absolute value ensures that the distance obtained is always positive, representing the perpendicular distance between the point and the line.

Q: How can the distance formula be applied to real-life scenarios?

The distance formula is used in various fields, such as physics, engineering, and computer graphics, where finding distances between points and lines is essential for solving problems and making calculations.

Summary & Key Takeaways

• The video explains the formula for calculating the distance between a point and a line in 2D and 3D.

• It demonstrates how to use the formula with provided values to find the distance.

• The process involves determining the coefficients for the line and substituting them into the formula along with the coordinates of the given point.