š Endpoint Calculator
Find the missing endpoint given one endpoint and the midpoint
Known Endpoint (xā, yā)
Midpoint (x_m, y_m)
How to Use This Calculator
Enter Known Endpoint
Input the coordinates (xā, yā) of one endpoint of the line segment.
Enter Midpoint
Input the coordinates (x_m, y_m) of the midpoint of the line segment.
Click Calculate
Press "Calculate Endpoint" to find the coordinates of the missing endpoint.
Formula
Given midpoint formula: (x_m, y_m) = ((xā + xā)/2, (yā + yā)/2)
Solving for endpoint: xā = 2x_m - xā, yā = 2y_m - yā
Where:
- (xā, yā) = Known endpoint
- (x_m, y_m) = Midpoint
- (xā, yā) = Unknown endpoint (to find)
Example: Endpoint (2, 3), Midpoint (5, 6)
xā = 2(5) - 2 = 10 - 2 = 8
yā = 2(6) - 3 = 12 - 3 = 9
Result: (8, 9)
About Endpoint Calculator
The Endpoint Calculator finds the missing endpoint of a line segment when you know one endpoint and the midpoint. It uses the midpoint formula rearranged to solve for the unknown endpoint.
When to Use This Calculator
- Geometry: Find missing endpoints in line segment problems
- Mathematics: Solve coordinate geometry problems
- Graphing: Determine endpoints when drawing line segments
- Engineering: Calculate positions from known points and midpoints
- Architecture: Find endpoint positions in design layouts
- Education: Learn and practice midpoint and endpoint concepts
Why Use Our Calculator?
- ā Simple Formula: Uses rearranged midpoint formula
- ā Step-by-Step Display: Shows the calculation process
- ā Works with All Numbers: Handles decimals, fractions, and negatives
- ā 100% Accurate: Precise mathematical calculations
- ā Educational: Helps understand midpoint-endpoint relationships
- ā Completely Free: No registration required
Understanding Endpoints and Midpoints
The midpoint is the center point of a line segment, equidistant from both endpoints. Given the midpoint formula and one endpoint, we can solve for the other endpoint.
- Midpoint formula: (x_m, y_m) = ((xā + xā)/2, (yā + yā)/2)
- Solving for xā: xā = 2x_m - xā
- Solving for yā: yā = 2y_m - yā
- The midpoint is exactly halfway between the two endpoints
- Both endpoints are equidistant from the midpoint
Real-World Applications
Construction: When laying out foundations or structures, if you know one corner point and the center point, you can find the opposite corner.
Navigation: In mapping and GPS, finding endpoints from known midpoints helps locate destinations or waypoints.
Design: Graphic designers use endpoint calculations to create symmetrical layouts and balanced compositions.
Frequently Asked Questions
How do I find an endpoint from a midpoint?
Use the formula: xā = 2x_m - xā and yā = 2y_m - yā, where (xā, yā) is the known endpoint and (x_m, y_m) is the midpoint. This is the midpoint formula rearranged.
What's the relationship between midpoint and endpoints?
The midpoint is exactly halfway between the two endpoints. It's the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Can I use this in 3D?
This calculator is for 2D coordinates. For 3D, use: xā = 2x_m - xā, yā = 2y_m - yā, zā = 2z_m - zā, where z is the third dimension.
What if the midpoint equals one endpoint?
If the midpoint equals one endpoint, then that endpoint is the midpoint, and the other endpoint is at the same location (degenerate line segment with zero length).
How accurate is this calculator?
This calculator provides precise results based on the exact mathematical formula. Accuracy depends on your input values and the precision of floating-point arithmetic.
Can endpoints be negative?
Yes! Endpoints can have negative coordinates. The formula works for all real numbers, including negatives, decimals, and fractions.
What's the difference from finding midpoint from endpoints?
This calculator does the reverse: given midpoint and one endpoint, find the other endpoint. To find midpoint from endpoints, use: (x_m, y_m) = ((xā + xā)/2, (yā + yā)/2).