Respuesta :
From the information given, GH is a straight line. One of its endpoints is (0,0).
This means that
x1 = 0, y1 = 0
We want to determine values for x2 and y2 that would give the longest possible length for GH.
The formula for determining the length of a line is expressed as
[tex]\text{length = }\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Looking at the above equation, the values of x2 and y2 that would give the longest possible length of GH would be x2 = - 2, y2 = 8
The length of the segment would be
[tex]\begin{gathered} \text{length = }\sqrt{(-2-0)^2+(8-0)^2} \\ \text{length = }\sqrt{68} \end{gathered}[/tex]If we input the other option, the length would be lesser than the one we got.
Therefore, the correct option is (- 2, 8)
