Hello!
Given the two points, [tex] (x_{1}, y_{1}) [/tex] and [tex] (x_{2}, y_{2}) [/tex], to find the length between these two points is found by using the formula:
[tex] d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}} [/tex]
[tex] (x_{1}, y_{1}) [/tex] is assigned to one the points, the first point can be assigned to (2, 5).
[tex] (x_{2}, y_{2}) [/tex] is assigned to other point, which is (9, 8).
Then, plug in these values into the formula and solve.
[tex] d = \sqrt{(9-2)^{2}+(8-5)^{2}} [/tex]
[tex] d = \sqrt{(7)^{2}+(3)^{2}} [/tex]
[tex] d = \sqrt{49 + 9} [/tex]
[tex] d = \sqrt{58} [/tex] or about [tex] d = 7.62 [/tex].
Therefore, the length of the line segment that joins the two points is √58.
