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Intersection Point

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

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Intersection Point -

Tag(s) : Functions

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# Intersection Point

## Find Intersection Point(s) of 2 Curves

Curves means any type of geometric function, lines included.

### What is an intersection point? (Definition)

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

### How to calculate the intersection point of 2 lines?

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).

### How to calculate the intersection point of 2 curves?

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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