Tool for finding the intersection point(s) of 2 lines or curves by calculation from their respective equations (crossing in the 2D plane).

Intersection Point - dCode

Tag(s) : Functions

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A point of intersection between 2 elements/drawings/graphs/curves in the 2D plane is the place of crossing/superposition of the 2 elements.

From the equations of the 2 lines of the 2D plane, it is possible to calculate the point of intersection (if it exists) by solving the corresponding system of equations. The values obtained (generally for $ x $ and $ y $) correspond to the coordinates $ (x, y) $ of the point of intersection.

__Example:__ The lines of respective equations $ y = x + 2 $ and $ y = 4-x $ form the system of equations $ \begin{cases} y = x+2 \\ y = -x+4 \end{cases} $ which has for solution $ \begin{cases} x = 1 \\ y = 3 \end{cases} $ therefore the point of intersection of the 2 lines is the point of coordinates $ (1,3) $

If the equations of the lines are not known, dCode allows you to find the equations of a line from its slope coefficient, its y-intercept or only from 2 points (linear equation).

The calculation of the point (or points) of intersection of 2 curves requires solving the corresponding system of equations.

__Example:__ The square function of equation $ y = x^2 $ and the horizontal line $ y = 1 $ allow to create the system of equations $ \begin{cases} y = x^2 \\ y = 1 \end{cases} $ which has 2 solutions $ \begin{cases} x = 1 \\ y = 1 \end{cases} $ and $ \begin{cases} x = -1 \\ y = 1 \end{cases} $ and therefore the square function has 2 points of intersection with the horizontal line at the coordinate points $ (x,y) $: $ (-1,1) $ and $ (1,1) $

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Cite as source (bibliography):

*Intersection Point* on dCode.fr [online website], retrieved on 2023-09-23,

intersection,point,crossing,coordinate,line,curve,equation,plane

https://www.dcode.fr/intersection-point

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