Lets suppose, we are given two different points (x1, y1) and (x2, y2). To find distance between these points, we can directly use the formula:
.
This formula is also called Distance formula.
Now, the question arises that from where did we get this formula to find the distance between two given points.
Suppose, A(x1, y1) and B(x2, y2) are two points as shown in the figure. We draw perpendicular AD to x axis and draw perpendicular BC to x axis. We then draw perpendicular BE to AD to complete a right angled triangle AEB.
Now, if we can know lengths of sides AE and BE then we can easily find distance AB by using pythagoras theorem.
Clearly, E =(x1, y2)
AE = y1 – y2
And, BE = x1 – x2
Applying, Pythagoras theorem to find AB, we have
This formula is also called distance formula.
Now, lets suppose P = (2,3) and Q = (5,6)
What is the distance between points P and Q?
Applying distance formula, we have
PQ =
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