# The length of the line segment connecting (2 -2) and (-3 -1) is

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Find the length of the line segment connecting (2,-2) and (-3,-1):

The distance formula for the distance between two points `(x_1,y_1),(x_2,y_2)` is `d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

**Thus the distance is `sqrt((-3-2)^2+(-1-(-2))^2)=sqrt(25+1)=sqrt(26)` **

The distance formula is really the Pythagorean theorem:

Let A be (2,-2) and B be (-3,-1). Then let C be (-3,-2). Then `bar(AB)` is the hypotenuse of right triangle ABC so `(AB)^2=(BC)^2+(AC)^2` where BC=-1-(-2)=1 and AC=|-3-2|=5 so `AB=sqrt(5^2+1^2)` as before.