Answer:
The coordinates of the rest stop are [tex](-\frac{9}{5},-4)[/tex].
Step-by-step explanation:
Given information: Tampa is located at (-3,-5) and Orlando at (3,0). The rest stop divides the way in the ratio 1:4.
Section formula:
If a line segments have two end points [tex]P(x_1,y_1)[/tex] and [tex]Q(x_2,y_2)[/tex] and a point divides the line PQ in m:n, then the coordinates of that point are
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
End points of the way are (-3,-5) and (3,0). Ratio is 1:4.
Using section formula we get
[tex](\frac{(1)(3)+(4)(-3)}{1+4},\frac{(1)(0)+(4)(-5)}{1+4})[/tex]
[tex](\frac{3-12}{5},\frac{0-20}{5})[/tex]
[tex](\frac{-9}{5},\frac{-20}{5})[/tex]
[tex](-\frac{9}{5},-4)[/tex]
Therefore the coordinates of the rest stop are [tex](-\frac{9}{5},-4)[/tex].
