Calculator Form
Use 2D for planar work. Use 3D for spatial vectors.
Example Data Table
| Mode | Point A | Point B | Midpoint | Direction Vector | Distance |
|---|---|---|---|---|---|
| 2D | (2, 3) | (8, 11) | (5, 7) | (6, 8) | 10 |
| 3D | (1, 2, 3) | (7, 6, 9) | (4, 4, 6) | (6, 4, 6) | 9.3808 |
| 2D | (-4, 5) | (6, -1) | (1, 2) | (10, -6) | 11.6619 |
Formula Used
Midpoint Formula
For 2D, midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
For 3D, midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2, (z₁ + z₂) / 2).
Direction Vector
Direction vector d = B - A.
So d = (x₂ - x₁, y₂ - y₁) in 2D, or d = (x₂ - x₁, y₂ - y₁, z₂ - z₁) in 3D.
Distance or Magnitude
|d| = √(dx² + dy²) for 2D.
|d| = √(dx² + dy² + dz²) for 3D.
Unit Vector
u = d / |d|.
This shows direction without changing scale.
Line Direction Details
In 2D, angle θ = atan2(dy, dx).
In 3D, direction angles use α = cos⁻¹(dx / |d|), β = cos⁻¹(dy / |d|), and γ = cos⁻¹(dz / |d|).
Parametric Form
r(t) = A + td.
This writes the whole line through both points.
How to Use This Calculator
Step 1: Choose 2D or 3D mode.
Step 2: Enter the coordinates for Point A.
Step 3: Enter the coordinates for Point B.
Step 4: Pick the decimal precision you want.
Step 5: Click the calculate button.
Step 6: Read the midpoint, direction, distance, and line data.
Step 7: Use the plot to verify the geometry visually.
Step 8: Export the result as CSV or PDF when needed.
Frequently Asked Questions
1. What does the midpoint represent?
The midpoint is the exact center of the segment connecting two points. It splits the segment into two equal lengths. This is useful in geometry, graphics, and engineering layouts.
2. What is a direction vector?
A direction vector points from the first coordinate to the second. It tells you how far to move along each axis. It is essential for line equations, transformations, and motion analysis.
3. Why does the calculator show a unit vector?
The unit vector keeps only direction and removes length. It is useful when you need standardized direction data for physics, navigation, and normalization tasks.
4. What happens if both points are identical?
The midpoint is still valid because both points match. The direction vector becomes zero, the distance becomes zero, and the unit vector is undefined because a zero vector has no unique direction.
5. Why is slope unavailable in 3D mode?
Slope is mainly a 2D idea based on rise over run. In 3D, direction is better described with vector components, direction cosines, and direction angles.
6. Can I use decimal and negative values?
Yes. The calculator accepts positive, negative, and decimal coordinates. That makes it suitable for classroom problems, coordinate geometry, and real measurement data.
7. What does the graph help me verify?
The graph lets you inspect both endpoints, the connecting segment, and the midpoint. It helps confirm direction, placement, and symmetry before using results elsewhere.
8. When should I export CSV or PDF?
Use CSV for spreadsheets, data logs, and repeated reporting. Use PDF for worksheets, project notes, and documents you want to share or print.