Difference between Midpoint and Endpoint Calculator

June 5, 2023

Difference between Midpoint and Endpoint Calculator

A midpoint is a point located halfway between two given points that are the endpoints of a line. This point divides the line into two equal parts.

Additionally, any line that bisects the segment joining the two endpoints must pass through the midpoint. The difference between Midpoint and Endpoint calculator is an important concept to understand when dealing with geometry and mathematical calculations.

The midpoint formula is utilized to find the midpoint of a line with known endpoint coordinates. This formula can also be used to calculate the coordinates of one endpoint if the midpoint and the other endpoint’s coordinates are known. There are various techniques available to find the midpoint of a line. Understanding the midpoint formula is one of them. Therefore, it is crucial to differentiate between these terms using a midpoint endpoint calculator to ensure accurate results.

Read more about: Difference between Distance and Midpoint Calculator

Midpoint Formula

The formula provides the midpoint coordinates of two points \((X_1, Y_1)\) and \((X_2, Y_2)\) on the coordinate plane.

Midpoint Formula

\((X, Y) = [\dfrac{(X_1 + X_2)}{2}, \dfrac{(Y_1 + Y_2)}{2}]\)

Midpoint on a Number line

Consider the following example, where we aim to find the midpoint of two points on a one-dimensional axis. Suppose we have 4 and 10 points located on a number line. We apply the formula to determine the midpoint between these two points:

\(\dfrac{4 + 10}{2} = \dfrac{14}{2} = 7\)

Therefore, 7 represents the midpoint of 4 and 10.

Midpoint on a Number line

Midpoint on a Horizontal Line

In the case of a vertical or horizontal line segment, we can divide its length by 2 and count that distance from either endpoint to locate the midpoint. For example, consider the diagram below, which shows the coordinates of two points, \(A (-4, 3)\) and \(B (2, 3)\), on a horizontal line segment. The length of segment AB is 6 units. By halving this length, we obtain a distance of 3 units. By counting 3 units from the initial point \((-4, 3)\), we arrive at the midpoint \((-1, 3)\). Therefore, the midpoint of AB is \((-1, 3)\).

Midpoint on a Horizontal Line

Endpoint Formula

The endpoint formula is closely related to the midpoint formula. The midpoint of a line segment, which lies at the centre or middle of the segment between its endpoints, can be determined using the midpoint formula. With one endpoint and the midpoint of the line segment given, the endpoint formula can then be used to find the other endpoint. Alternatively, you can find endpoint calculator here for quick calculations.

The endpoints mark the start and end points of a line segment or the stopping point of a ray, beyond which the line does not extend any further. The midpoint lies at the centre of the endpoints, and to calculate the endpoints, we need to use the midpoint formula.

Assuming that \(M ((X)_m, (Y)_m)\) is the midpoint of a line segment joining two endpoints, \(A ((X)_1, (Y)_1)\) and \(B ((X)_2, (Y)_2)\), we can apply the midpoint formula to solve for either of the endpoints. Given the coordinates of M and A, the endpoint formula can be used to calculate the coordinates of B using the following equation:

Midpoint Formula for Calculating the Endpoints

\((X)_m = \dfrac{(X_1 + X_2)}{2} \) and \( (Y)m = \dfrac{(Y_1 + Y_2)}{2}\)

\((X)_2 = 2(X)_m – (X)_1 \) and \( (Y)_2= 2(Y)_m-Y_1\)

Thus, the endpoint formula is,

Endpoint formula of \(B((X)_2,(Y)_2) = (2(X)_m-(X)_1 , 2(Y)_m-(Y)_1)\)

Midpoint Formula for Calculating the Endpoints

Conclusion:

A midpoint and endpoint calculator is useful for finding the midpoint or endpoint of a line segment. The midpoint formula calculates the middle point of a line segment by averaging its endpoints’ X and Y coordinates. The formula is widely used in geometry, physics, and engineering. The endpoint formula, derived from the midpoint formula, helps find one endpoint’s coordinates if the midpoint and the other endpoint are known.

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