Distance from a point to a line

Autor:Bradford L Dalton, Mathguru

Tema:Álgebra, Geometría, Intersección, Ecuaciones lineales, Rectas, Matemática, Pitágoras o Teorema de Pitágoras, Triángulos Rectángulos

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.