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Geometry: Distance Formula

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Usually the coordinate place consists of two axes namely X axis and Y axis. Thus, a point in a coordinate plane is usually denoted by the coordinates (x,y) where x is the perpendicular distance of the point from Y-axis and y is the perpendicular distance from the X-axis as shown below.

Thus we can easily find the distance of a point from the axes just by seeing the x and y coordinates. But, how to find the distance between two points when their coordinates are given? We use Pythagoras theorem to find the distance between two points.

Let P (x1,y1) and Q (x2,y2) be any two points in a plane. Let us find the distance between them PQ.

Then from the figure, we get

PR = |x2-x1| and QR = |y2-y1|.

We know that the Pythagoras theorem states, “In a right angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides”.’

According to this theorem, we have

PQ2 = PR2 + QR2

PQ2 = |x2-x1| 2 + |y2-y1|.2

Taking square root on both sides, we get

PQ = √(|x2-x1| 2 + |y2-y1|2)

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