\[\begin{aligned}
d &= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\
M_x &= \frac{x_1+x_2}{2} \\
M_y &= \frac{y_1+y_2}{2}
\end{aligned}\]
Variables
ddistance between points
Mxmidpoint x-coordinate
Mymidpoint y-coordinate
x1x-coordinate of first point
y1y-coordinate of first point
x2x-coordinate of second point
y2y-coordinate of second point
Description
What is this formula?
This set of formulas calculates the distance and midpoint between two points in a Cartesian coordinate system.
When to use it
Use these formulas in geometry, coordinate analysis, engineering, physics, navigation, and computer graphics whenever point positions must be analyzed.
Example
For points (1,2) and (5,6):
Distance:
d = √((5-1)²+(6-2)²)
d = √(16+16)
d ≈ 5.66
Midpoint:
Mx = (1+5)/2 = 3
My = (2+6)/2 = 4
Applications
- Coordinate geometry
- CAD and computer graphics
- Navigation systems
- Physics and vector analysis
- Engineering calculations