# The Midpoint Formula

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A 2-dimensional coordinate plane consists of X and Y axis and in this plane any point can be located by representing it through the ‘x’ and ‘y’ coordinates. If a line is joining two points represented as (x1, y1) and (x2, y2), then we can find the midpoint of the line using the formula: [(x1 + x2)/2, (y1 + y2)/2]. This midpoint formula helps us calculate the coordinate of the point which lies in the middle of any line in the 2-dimensional coordinate plane.

Example 1: Find the midpoint of the line whose endpoints of the line are A (2, 3) and B (4, 5).

Given points: A (2, 3) and B (4, 5)

Midpoint of a line, (x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Here given point A= (x1, y1) = (2, 3) and point B= (x2, y2) = (4, 5)

This gives: midpoint of the line AB = (x, y) = [(2+ 4)/2, (3+ 5)/2] = (6/2, 8/2) = (3, 4)

Hence the midpoint of the given line AB is (3, 4).

Example 2: Find the midpoint of the line whose endpoints of the line are X (-1, 4) and Y(3, -6).

Given points: X (-1, 4) and Y (3, -6)

Midpoint of a line, (x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Here given point X= (x1, y1) = (-1, 4) and point Y= (x2, y2) = (3, -6)

This gives: midpoint of the line XY = (x, y) = [(-1 + 3)/2, (4+ (- 6))/2] = (2/2, -2/2) = (1, -1)

Hence the midpoint of the given line XY is (1, -1).