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# Midpoint of an Interval

Midpoint of an interval, i.e. two points A (x1, y1) and B (x2, y2) is obtained by finding the mid value along x and y coordinates separately.

So the midpoint along the x axis = and the midpoint along the y axis = .

Therefore midpoint of the line AB is ## Examples of midpoint of an interval

Example 1: Find the midpoint of A (-3, 2) and B (3, 5)

Midpoint of AB  = = = Example 2: ABCD is a quadrilateral with coordinates A(1, -1), B(3, 5), C(7, 7) and D(5, 1). Find the midpoints of AC and BD to prove ABCD is a parallelogram.

Midpoint of AC  = = = Midpoint of BD  = = = The midpoints off the diagonals AC and BD are both (4, 3). Hence the diagonals bisect each other. Therefore ABCD is a parallelogram.

Example 3: The point M(3, 5) is the midpoint of the interval AB where A is the point (-1, 2). Find the coordinates of B. Here we’ve been given the midpoint and one of the coordinates, and need to find the other coordinate.

Midpoint of an interval = 3 = 6 = -1 + x2

x2 = 7

5 = 10 = 2 + y2

y2 = 10 – 2  =  8

B(x2, y2)  is B(7, 8)