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You wish to take a flight from Nevada to New York. Use the point (-4,0) to represent Nevada, aand the (5,2) to represent New York. The airline had partitioned the flight so that you have a layover. The flight distance is partitioned in a ratio 3:2. Determine the ordered pair that represents the location of the layover. What state will you be in when you have the layover?

You Wish To Take A Flight From Nevada To New York Use The Point 40 To Represent Nevada Aand The 52 To Represent New York The Airline Had Partitioned The Flight class=

Sagot :

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.

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