Distance from a point to a line

Author:Bradford L Dalton, Mathguru

Topic:Algebra, Geometry, Intersection, Linear Equations, Straight Lines, Mathematics, Pythagoras or Pythagorean Theorem, Right Triangles

Explanation

We can clearly see the graph of line BC is shown in red colors and its equation is written in the form y=mx+b. This line passes through two points (blue) B and C. Point A is present on the coordinate plane and its coordinates are (x1, y1). D is the intersection of the perpendicular line segment DA with the line BC. Length of the line segment DA (green) is equal to the distance of point A from the line BC. We can move these three free points A, B and C and observe how the position of line BC( and equation)and the length of AD change.

distance of a point from a line

Explore

In the graph above move the points around to explore different position of the perpendicular line and the line it intersects with

The shortest distance from a point to a line

1. ) What is the shortest distance from a point to a line? Discuss and explain fully.

distance of a point from a line

2.) Move the line to have it with a slope of -1 and a y-intercept of 1

What is the slope of the perpendicular line segmant?

3.) Now move the perpendicular so that A is on the coodinate A(3,5)

The distance is shown BUT how can you calculate this distance on the coordinate plane? Explain and discuss

distance of a point from a line

Explanation

If a point is off of a line then you can find the distance from the line by making sure it is on the perpendicular line through that point to the line. Now lets work a few problems involving that fact and a series of steps that is one way you can achieve this goal

Predict

Talk with your group and see if you can come up with a way to find a method Explain below.