The location of the point F that partitions a line segment from D to E ([tex]\overline{DE}[/tex]), that goes from negative 4 to positive 5, into a 5:6 ratio is fifteen halves (option 4).
We need to calculate the segment of the line DE to find the location of point F.
Since point D is located at negative -4 and point E is at positive 5, we have:
[tex] \overline{DE} = E - D = 5 - (-4) = 9 [/tex]
Hence, the segment of the line DE ([tex]\overline{DE}[/tex]) is 9.
Knowing that point F partitions the line segment from D to E ([tex]\overline{DE}[/tex]) into a 5:6 ratio, its location would be:
[tex] F = \frac{5}{6}\overline{DE} = \frac{5}{6}9 = 5*\frac{3}{2} = \frac{15}{2} [/tex]
Therefore, the location of point F is fifteen halves (option 4).
Learn more about segments here:
- https://brainly.com/question/24472171?referrer=searchResults
- https://brainly.com/question/13270900?referrer=searchResults
I hope it helps you!
