Question

The locations in a city are mapped out on a grid, where the origin represents the city center. A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).
About how many fewer units would the helicopter have traveled if it went directly from one location to the other?

Answer 1

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:

$(x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Distance traveled by helicopter =

$d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}$

If the helicopter goes directly:

$d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}$

Difference in distances =

$19 - 13.45 = 5.55\text{ units}$

Thus, helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.