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Distance Between Two Points:

A.  To find the distance between two points: (x₀,y₀) and (x₁,y₁) use the following formula:

B.  Many times this type of problem can be done quicker if you know common Pythagorean Triples.

C.  Examples

Ex [1]  The distance between (-2,4) and (3,-8) is ______.

a.  In this problem we should subtract the x-values first.  So -2 - 3 = -5.

b.  After subtracting the y-values we get: 4 - (-8) = 4+8 = 12.

c.  You should know the Pythagorean Triple: (5,12,13).  The answer is 13.  If you don't know this you can see that .

Ex [2]  The distance between (1,-3) and (7,5) is ______.

a.  Subtracting the x-values we get 1 - 7 = -6.

b.  Subtracting the y-values we get -3 - 5 = -8.

c.  You should know the Pythagorean Triple: (6,8,10).  The answer is 10.  If you don't know this you can see that .

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