Midpoint Formula

About Midpoint Formula

A midpoint is a point in the middle of a line that connects two points. The endpoints of a line are the two reference points, and the midway is located in the middle. The midway splits the line that connects these two places in half. In addition, a line drawn to bisect the line connecting these two places passes through the midway.

To get the midway between two places whose coordinates are known, we utilise the midpoint formula. If we know the coordinates of the other endpoint & the midpoint, we can apply the midpoint formula to obtain the coordinates of the endpoint. If a line is created in the coordinate plane to connect two points (5, 3) and (9, 7), the coordinates of the midpoint of the line connecting these two points are ({5 + 9}/2, {3 + 7}/2) = (14/2, 10/2) = (7, 5). Let's study more about the midpoint formula and alternative approaches for locating a line's midpoint.

What is Midpoint?

A midpoint is a point in middle of a line that connects two points. If the two points are connected by a line, the midpoint is a position in the middle of the line that is equidistant from both. The midpoint is a point B that is midway between two points, such as A and C. To find the midway, simply divide the line segment length by two.

Point B is equidistant from points A and C. A line segment's midpoint is unique. Because a line is indefinite in both directions and a ray has just one end and can thus be stretched, neither can have a middle.

Midpoint Formula

The midpoint formula is defined for the points in the coordinate axes. Let (x)1, (y)1 and (x)2, (y)2 be the endpoints of a line segment. The midpoint is equal to half of the sum of the two points' x-coordinates and half of the sum of the two points' y-coordinates. The formula for calculating the midpoint of a line segment connecting these places is as follows:

Midpoint Formula (Maths)

Given 2 points A (x)1, (y)1 & B (x)2, (y)2, the midpoint between A & B is -M(x)3, (y)3 = [(x)1 + (x)2]/2, [(y)1 + (y)2]/2

where, M is the midpoint between A & B, and (x)3, (y)3 are its co-ordinates.

If, we have 2 points, 6 & 10, on a number line. The midpoint will be calculated as: (6 + 10)/2 = 16/2 = 8. So, 8 is the midpoint of 6 & 10.

Formulas Related to Midpoint

The midpoint formula comprises separate computations for the x-coordinate and the y-coordinate of the points. Furthermore, computations of points between two provided points include identical computations of the given points' x- and y-coordinates. The midpoint formula is closely connected to the following two formulas.

  • Centroid of Triangle Formula
  • Section Formula

The centroid of a Triangle Formula

The centroid of a triangle is the place where the medians of the triangle intersect. The median is a line that connects the vertex to the opposite side of the triangle's midpoint. The triangle's median is divided by the centroid in a 2:1 ratio.

Triangle with the vertices (x)1, (y)1, (x)2, (y)2, (x)3, (y)3 the formula to find the coordinates of the centroid of the triangle is as follows.

Section Formula

The section formula can be used to calculate the coordinates of any point on the line connecting two points. In addition, knowing the coordinates of the point requires knowing the ratio in which the point divided the line connecting the two supplied points. The point might be between the points or beyond them, but it must be on the same line. The following is the section formula for determining a point's coordinates, which splits the line joining the points (x)1, (y)1, and (x)2, (y)2 in the ratio m:n. The positive sign is used in the formula to get the coordinates of a point that divides the points internally, while the negative sign is used if the point divides the points externally

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