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Endpoint Calculator

Enter the coordinates of the starting point and midpoint, and the tool will quickly calculate the endpoint coordinates.

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The Endpoint Calculator allows you to determine the missing endpoint of a line segment when one endpoint and the midpoint are known. It can also plot the start point, midpoint, and endpoint on a coordinate graph, making visualization easy and accurate.

What is an Endpoint?

An endpoint is a point that marks the end of a line segment or the starting point of a ray. For a line segment, the segment stops at its endpoints, whereas for a ray, the line extends infinitely from its endpoint. Simply put, an endpoint is defined as “the terminal point of a line or segment.”

Endpoint Formula

If you know one endpoint (x1, y1) and the midpoint (x, y), the other endpoint (x2, y2) can be calculated using the formula:

x2 = 2*x - x1

y2 = 2*y - y1

Where:

(x2, y2) are the coordinates of the unknown endpoint.
(x1, y1) are the coordinates of the known endpoint.
(x, y) are the coordinates of the midpoint.

How to Use the Endpoint Calculator

This calculator helps you quickly find the missing endpoint of a line segment in coordinate geometry.

Inputs:

Coordinates of the starting point (x1, y1).
Coordinates of the midpoint (x, y).
Click "Calculate" to find the missing endpoint.

Outputs:

Coordinates of the missing endpoint.
Step-by-step calculation of the endpoint.
Distance between the two endpoints.
Step-by-step distance calculation.
Graph of the line segment showing all points.

Step-by-Step Example

Here is an example of using the endpoint formula manually:

Example:

Given starting point (3, 7) and midpoint (-5, 2), find the missing endpoint.

Solution:

Step 1: Identify coordinates:

x1 = 3, y1 = 7

Midpoint: x = -5, y = 2

Step 2: Calculate x2:

x2 = 2*x - x1

x2 = 2*(-5) - 3

x2 = -10 - 3

x2 = -13

Step 3: Calculate y2:

y2 = 2*y - y1

y2 = 2*2 - 7

y2 = 4 - 7

y2 = -3

Step 4: Missing endpoint coordinates:

(x2, y2) = (-13, -3)

Frequently Asked Questions (FAQs)

How do you calculate the length of a line segment?

Use the distance formula: $$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$. For example, for points (-4, 5) and (-6, 9), the distance is approximately 4.47 units.

How do you find the difference between two points?

The difference is calculated using the distance formula, which involves the square root of the sum of squared differences in x and y coordinates. Learn more.

How many endpoints does a line segment have?

A line segment has exactly two endpoints. Points in between are part of the segment but do not count as endpoints. Learn more.

References

Source: Math.net - Endpoints. Source: _

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