To answer this question we will use the following formulas to compute the coordinates of the point that divides a segment with terminal points (x₁,y₁) and (x₂,y₂) at a given ratio a:b:
[tex]\begin{gathered} x=\frac{bx_1+ax_2}{b+a}, \\ y=\frac{by_1_{}+ay_2}{b+a}\text{.} \end{gathered}[/tex]
Therefore, the coordinates that represent the location of the layover are:
[tex]\begin{gathered} x=\frac{2\times(-4)+3\times5}{2+3}, \\ y=\frac{2\times0+3\times2}{2+3}\text{.} \end{gathered}[/tex]
Simplifying the above results we get:
[tex]\begin{gathered} x=\frac{-8+15}{5}=\frac{7}{5}=1.4, \\ y=\frac{0+6}{5}=\frac{6}{5}=1.2. \end{gathered}[/tex]
Now, from the given map, we get that the point (1.4,1.2) is on Iowa.
Answer:
The ordered pair that represents the location of the layover is:
[tex]\mleft(1.4,1.2\mright)\text{.}[/tex]
The state at which we will be during the layover is Iowa.
