Answer:
Helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.
Step-by-step explanation:
We are given the following in the question:
A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).
The attached image shows the path of helicopter.
Distance Formula:
[tex](x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Distance traveled by helicopter =
[tex]d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}[/tex]
If the helicopter goes directly:
[tex]d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}[/tex]
Difference in distances =
[tex]19 - 13.45 = 5.55\text{ units}[/tex]
Thus, helicopter have traveled 5.55 units of distance approximately if it went directly from one location to the other.
