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

embizze | Certified Educator

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.

vaaruni | Student
Let the points connecting the line segment be A(x1,y1)and B(x2,y2) Here given (x1,y1)=(2,-2) and (x2,y2)=(-3,-1) The formula for the length of the line segment AB joining the poinpoints A(x1,y1) and B(x2,y2) = sqrt((x2-x1)^2 + (y2-y1)^2)) Using the above formula : AB = sqrt((x2-x1)^2 + (y2-y1)^2)) => AB = sqrt((-3-(2))^2 + ((-1)-(-2))^2 ) => AB = sqrt((-2-3)^2 + (-1+2)^2 ) => AB = sqrt((-5)^2 + (1)^2 ) => AB = sqrt(25+1) => AB = sqrt(26) => AB = 5.09 <-- Answer