Lines

Define by the equation

r = x + y =

Define by two points

A=(,)
B=(,)

Define by a point and a vector

A=(,)
B=(,)

P=(,)

Help

Show help

Aim of the applet

Manage various constructions of a line and display parallel and perpendicular to a line.

Input data

The line can be defined in three ways:

By equation: The user can entercoefficients that define the line.
By two points: The user can enter two points A and B for which the line must pass. Also, the user can move the points A and B directly on the graph by the mouse.
By a point and a vector: The line passes through the point P with the direction of vector AB, given by points A and B.

Output data

The graph can show the graphic representation of the equation of the following elements:

Line defined by the user.
Perpendicular line through point C.
Parallel line through point C.

Using the mouse you can change both the points as vectors, so that the line is updated dynamically.

First steps

Built the line through the points A = (2.0) and B = (2,4). Calculate the perpendicular passing through point C = (6,6).
Draw the line y =- 6. Write two points and a direction vector and get the equation from the 2 points and the vector to see what is y =- 6.
You can get the slope of a line solving y = mx + n. Calculates perpendicular line to 3x + 2y = 2. Then, on paper, calculated the slopes m and m 'of both and see m =- 1 / m'.