# The Distance Formula

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Distance formula is the formula used to measure the distance between any two points on a coordinate plane. On the coordinate plane, points are plotted using the X axis and the Y-axis and the distance formula is very useful in finding the distance between any two points on the plane. Let any two points on the coordinate plane be (x1, y1) and (x2, y2), then the distance between these points is given as: d = √[(x2 – x1)2 + (y2 – y1)2].

Example 1: What is the distance between the points A(1, 2) and B(1, 5)?

The distance formula is: d = √[(x2 – x1)2 + (y2 – y1)2]

Here given point A= (x1, y1)= (1, 2) and point B= (x2, y2)= (1, 5)

In order to find the distance between points A and B, we use the distance formula.

Distance, AB= √ [(1 – 1)2+ (5 – 2)2] = √ [(0 + (3)2]

Now we get, distance AB= √9= 3

Therefore the distance between points A and B is 3 units.

Example 2: What is the distance between the points P(2, 3) and Q(5, 4)?

The distance formula is: d = √ [(x2 – x1)2 + (y2 – y1)2]

Here given point P= (x1, y1)= (2, 3) and point Q= (x2, y2)= (5, 4)

In order to find the distance between points P and Q, we use the distance formula.

Distance, PQ= √ [(5 – 2)2+ (4 – 3)2] = √ [(3)2 + (1)2]

Now we get, distance PQ= √(9+ 1)= √10.

Therefore the distance between points P and Q is √10 units.