Looking for a quick and easy way to calculate the endpoint of a line segment? Our simple Endpoint Calculator does the work for you. No need to deal with complex formulas — just enter the starting point and midpoint, and get the endpoint instantly.
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What is a Endpoint of a Line Segment?
An endpoint of a line segment is one of the two fixed points where the segment starts or ends. It defines the limits of the segment, meaning the line does not continue beyond these points. Every line segment has two endpoints, which separate it from a line that extends endlessly in both directions. Endpoints are important in geometry because they help define the length and position of the line segment.
Formula to Find End Point of Line Segment
For a line segment with given endpoint (x1, y1) and the midpoint (x, y), the formula to find the endpoint (x2, y2) is:
Our endpoint calculator simplifies this process for you, offering results in both fractional and decimal formats.
How to Use
- The use of this endpoint calculator is very simple.
- To find the endpoint of a line segment, you need to input the x-coordinate and y-coordinate of its one endpoint and midpoint in the respective fields.
- Once you provide these coordinates, the tool will display the midpoint’s ‘X2‘ and ‘Y2‘ coordinates.
Finding Endpoint – Examples with Solutions
We have solved two examples of finding the endpoint of a line segment using its one endpoint and midpoint. These examples will help you understand how to apply the endpoint formula.
Example :
1. Find the endpoint of a line segment if the starting point (X₁, Y₁) is (2, 3) and the midpoint (X, Y) is (5, 7).
Solution :
To find the endpoint of the line segment with starting point (2, 3) and (5,7), we use the endpoint formula.
Endpoint (X₂, Y₂) = (2X – X₁, 2Y – Y₁)
Substitute the coordinates:
x = 5
y = 7
x1 = 2
y1 = 3
Calculate the x and y-coordinate of the endpoint:
Endpoint = [(2 × 5) – 2] , [(2 × 7) – 3]
Endpoint = (8, 11)
Result:
The endpoint (X₂, Y₂) is (8, 11).
Example :
2. Find the endpoint of a line segment if the starting point (X₁, Y₁) is (-3, 4) and the midpoint (X, Y) is (2, -1).
Solution :
To find the endpoint of the line segment with starting point (-3, 4) and midpoint (2, -1), we use the endpoint formula.
Endpoint (X₂, Y₂) = (2X – X₁, 2Y – Y₁)
Substitute the coordinates:
x = 2
y = -1
x1 = -3
y1 = 4
Calculate the x and y-coordinate of the endpoint:
Endpoint = [(2 × 2) – (-3)] , [(2 × -1) – 4]
Endpoint = [4 – (-3)] , [(-2) – 4]
Endpoint = [7 , [-6]
Endpoint = (7, -6)
Result:
The endpoint (X₂, Y₂) is (7, -6).
What is a Line Segment Endpoint?
A line segment endpoint is one of the two fixed points where a line segment begins or ends. Unlike a line, which extends infinitely in both directions, a line segment has a clear start and stop. These two endpoints define the length and position of the segment. For example, in a segment connecting points (2, 3) and (6, 7), the points (2, 3) and (6, 7) are the endpoints.
Can I Calculate the Endpoint Without a Midpoint?
No, you cannot calculate the endpoint without a midpoint if you’re using the standard endpoint formula. The formula relies on the midpoint to find the missing endpoint. However, if you have other information like the slope, direction, or length of the line, there are alternative methods to find the endpoint such as using slope and endpoint or distance and endpoint.