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Coordinate geometry

# Distance between two points in the plane

The distance between two points, A, and B, can be expresssed in terms of their coordinates by using the Pythagorean theorem. Let the coordinates of A, be (x1,y1) and let those of B be (x2,y2), as shown in figure:

By the Pythagorean theorem, the distance between two points A=(x1,y1) and B=(x2,y2) in the plane is given by the formula:

The distance between A=(-2,5) and B=(6,12) is given by:

Find the distance between the points A=(-5,6) and B=(1,-2)

D =