find the length of the segment. round to two decimal places if necessary.

Answer

First, assume the two - endpoints of the line segment:
- Let's assume the endpoints of the line segment are ((x_1,y_1)) and ((x_2,y_2)). From the graph, if we assume one endpoint is ((- 4,-10)) and the other is ((7,0)).
- The distance formula between two points ((x_1,y_1)) and ((x_2,y_2)) is (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}).
Then, substitute the values of (x_1,y_1,x_2,y_2) into the formula:
- Here, (x_1=-4,y_1 = - 10,x_2 = 7,y_2 = 0).
- First, calculate ((x_2 - x_1)) and ((y_2 - y_1)):
  - (x_2 - x_1=7-(-4)=7 + 4=11).
  - (y_2 - y_1=0-(-10)=0 + 10 = 10).
- Then, calculate ((x_2 - x_1)^2+(y_2 - y_1)^2):
  - ((x_2 - x_1)^2+(y_2 - y_1)^2=11^2+10^2=121 + 100=221).
- Finally, calculate the distance (d):
  - (d=\sqrt{221}\approx14.87).

Assume endpoints ((-4,-10)) and ((7,0))

(d=\sqrt{(7-(-4))^2+(0 - (-10))^2}=\sqrt{(7 + 4)^2+(0 + 10)^2}=\sqrt{11^2+10^2})

(11^2+10^2=121 + 100 = 221), so (d=\sqrt{221})

(d\approx14.87)

(14.87)