Question

Let A, B, C be the points (2, 3), (3, -2) and (-1, 4). Find the length of AB

Answer 1

Distance formula! d=distance, can be substituted with any length like AB or BC or whatever.

\[d=\sqrt{(x _{1}-x_{2})^2+(y_{1}-y_{2})^2}\]
The subscript is just to be sure you are consistent with your points. (i.e. match up the positions of your coordinates)

In your case, you need the distance between A(2,3) and B(3,-2). Let's use A for our first coordinate set and B for our second.

d=sqrt[(2-x)^2+(3-y)^2]
d=sqrt[(2-3)^2+(3-(-2))^2]
d=sqrt[(-1)^2+(5)^2]
d=sqrt[1+25]
d=sqrt[26]

AB=sqrt(26)

Answer 2

lenght of AB = \[\sqrt{26}\]