Answer:
a. Emily should begin her turn as the third driver at point (1, -0.5).
b. Emily's turn to drive end at point (-2.5, -3.75).
Step-by-step explanation:
Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:
Hometown
[tex]H(x,y) = (8,6)[/tex]
San Antonio
[tex]T(x,y) = (-6,-7)[/tex]
Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:
Steph
[tex]S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)][/tex] (1)
[tex]S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]S(x,y) = (8,6) +\frac{1}{4}\cdot (-14,-13)[/tex]
[tex]S(x,y) = (4.5,2.75)[/tex]
Andra
[tex]A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)][/tex] (2)
[tex]A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]A(x,y) = (8,6)+\frac{2}{4}\cdot (-14,-13)[/tex]
[tex]A(x,y) =(1, -0.5)[/tex]
Emily
[tex]E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)][/tex] (3)
[tex]E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]E(x,y) = (8,6)+\frac{3}{4}\cdot (-14,-13)[/tex]
[tex]E(x,y) = (-2.5, -3.75)[/tex]
a. If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver?
Emily's beginning point is the Andra's stop point, that is, [tex]A(x,y) =(1, -0.5)[/tex].
Emily should begin her turn as the third driver at point (1, -0.5).
b. At what point does Emily's turn to drive end?
Emily's turn to drive end at point (-2.5, -3.75).
