Endpoint Calculator
Find missing endpoints, midpoints, or starting points of line segments
Calculation Mode
What do you want to find?
Starting Point A (x₁, y₁)
Midpoint M (x, y)
Calculation Results
Step-by-Step Solution
Example Calculation
YouTube Channel Growth Example
Problem: You started a YouTube channel 4 months ago with 0 subscribers. Now you have 54,000 subscribers. If growth continues linearly, how many will you have in 4 more months?
Starting point: Month 0, 0 subscribers → A = (0, 0)
Current position (midpoint): Month 4, 54,000 subscribers → M = (4, 54000)
Goal: Find endpoint at month 8
Solution
Step 1: Use endpoint formula: B = (2x - x₁, 2y - y₁)
Step 2: Substitute values: B = (2×4 - 0, 2×54000 - 0)
Step 3: Calculate: B = (8, 108000)
Result: You'll have 108,000 subscribers in month 8!
Formula Reference
Find Endpoint
B = (2x - x₁, 2y - y₁)
Given: Starting point A(x₁,y₁) + Midpoint M(x,y)
Find Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Given: Starting point A(x₁,y₁) + Endpoint B(x₂,y₂)
Find Starting Point
A = (2x - x₂, 2y - y₂)
Given: Midpoint M(x,y) + Endpoint B(x₂,y₂)
Quick Tips
The midpoint is exactly halfway between two endpoints
Distance from start to midpoint = Distance from midpoint to end
All three points (start, mid, end) lie on the same straight line
Works for any coordinate system (negative numbers allowed)
Useful for linear growth predictions and geometry problems
Understanding Endpoints and Midpoints
What is an Endpoint?
An endpoint is a point that lies at the end of a line segment. Every line segment has exactly two endpoints (unless it's a degenerate case where both endpoints are the same point). Endpoints define the boundaries of the segment.
What is a Midpoint?
A midpoint is the point that lies exactly in the middle of a line segment. It divides the segment into two equal parts. The distance from one endpoint to the midpoint equals the distance from the midpoint to the other endpoint.
Real-World Applications
- •Linear growth prediction (business, population)
- •Finding center points in construction
- •Navigation and GPS coordinates
- •Computer graphics and animation
Mathematical Properties
Symmetry: If M is the midpoint of AB, then AM = MB
Collinearity: Endpoints and midpoint lie on the same line
Reversibility: Any of the three points can be calculated from the other two
Geometric Interpretation
When you have a line segment, the midpoint creates two smaller segments of equal length. This property is fundamental in geometry and has applications in coordinate geometry, vector mathematics, and analytic geometry.
Key Insight: The endpoint formula essentially "reflects" one endpoint across the midpoint to find the other endpoint. This is why we multiply the midpoint coordinates by 2 and subtract the known endpoint.
Common Use Cases
Business Growth
Predict future values based on linear growth patterns
- • Revenue forecasting
- • Customer acquisition
- • Market expansion
- • Performance metrics
Engineering & Design
Find center points and balance points in construction
- • Structural center points
- • CAD design
- • Architecture planning
- • Load distribution
Navigation & Mapping
Calculate intermediate points and destinations
- • GPS waypoints
- • Route planning
- • Geographic analysis
- • Location services