Distance Formula

Notation

Since we are working with two points we use special notation to distinguish between the points. One point we will label (x1 , y1) and the other point will be labeled (x2 , y2 ). It does not matter how you label either point. For our example I will label (1, 2) as (x1 ,y1 ) and (4, 3) as (x2 ,y2 ). The rest is just placing the values into the correct location of the formula.

A line segment with point A at (1, 2) and point B at (4, 3)

 

The formula for finding the distance between two points on a coordinate plane is given below. We’ll talk more about where this formula comes from later.

The distance formula. D is equal to the square root of (the distance between the x values squared plus the distance between the y values squared)

d equals the square root of [ (4 - 1) squared plus (3 - 2) squared ]

d equals the square root of ( 3 squared plus 1 squared)

d equals the square root of (9 + 1)

d equals the square root of 10

d = 3.2

Check It!

Distance Formula Example #2

Find the distance between the points (6,1) and (-2,5). Round your answer to the nearest tenths place.

Let’s walk through step by step. If (6,1) is (x1, y1) and (-2,5) is (x2, y2), fill in the first line below.

The distance formula. D is equal to the square root of (the distance between the x values squared plus the distance between the y values squared)

d equals the square root of [ ( -2 - 6) squared plus (5 - 1) squared ]

d equals ( -8 squared plus 4 squared)

d equals square root of (64 + 16)

d equals square root of 80

d = 8.9

Check It!

Segment and Distance

Although football was used in the Explore to discuss distance, a football field is not a good example of a number line.

0 10 20 30 40 50 40 30 20 10 0

You could count by 10’s on the number line but why doesn’t absolute value of the difference work?

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