Given the endpoints of a line segment fg is f(2,-7) and g(-7,8).

We need to find the length of the line fg.

We will use the distance between two points formula to calculate the length.

We know that:

D = sqrt[ (x1-x2)^2 + (y1-y2)^2 ]

==> l fg l = sqrt[(2+7)^2 + (-7-8)^2'

==> l fg l = sqrt[ (9^2 + (-15)^2 ]

==> l fg l = sqrt(81+225)

==> l fg l = sqrt(306) = 17.49

**Then the length of the line segment fg is sqrt(306)=17.49 units.**

We have to determine the length of the segment fg given f(2, -7) and g(-7, 8)

The distance between two points (x1, y1) and (x2, y2) is sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Substituting the coordinates of f and g we get the length of fg as

sqrt[( 2 + 7)^2 + (-7 - 8)^2]

=> sqrt [ 9^2 + 15^2]

=> sqrt (81 + 225)

=> sqrt 306

**The length of fg is sqrt 306.**