Distance Formula

In the coordinate plane, you can use the Pythagorean Theorem to find the distance between any two points.

The distance between the two points (x₁,y₁) and (x₂,y₂) is given by the distance formula.

Example:

To find the distance between the points P(2, 3) and Q(1, 1). We can sketch the right-angled triangle PQR with PQ as the hypotenuse.

Solution:
Using Pythagoras theorem: PQ2 = (2 – 1)2 + (3 –1)2
   Þ PQ =

In general, the distance between two points P(x1,y1) and Q(x2,y2) is given by the distance formula:

Example:
Find the distance between the points A(1, 2) and B(-3, -2).

Solution:
Using the distance formula:
Distance =
                   = 5.66 (correct to 2 decimal places)

The following video gives another example of using the distance formula.

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