a) The fire is out of the reach of helicopter 1.
b) Only helicopter 3 can be sent to stop the fire.
What helicopter does stop the fire?
We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:
- Fire - (x, y) = (- 3, - 5)
- Helicopter 1 - (x, y) = (1, 4)
- Helicopter 2 - (x, y) = (- 2, 3)
- Helicopter 3 - (x, y) = (4, - 2)
The distance is found by the straight line distance formula, an application of Pythagorean theorem:
a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]
[tex]d = \sqrt{4^{2}+9^{2}}[/tex]
[tex]d = \sqrt{97}[/tex]
d ≈ 9.849
The fire is out of the reach of helicopter 1.
b) Helicopter 2
[tex]d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}[/tex]
[tex]d = \sqrt{1^{2}+8^{2}}[/tex]
[tex]d = \sqrt{65}[/tex]
d ≈ 8.062
Helicopter 3
[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]
[tex]d = \sqrt{7^{2}+3^{2}}[/tex]
[tex]d = \sqrt{58}[/tex]
d ≈ 7.616
Only helicopter 3 can be sent to stop the fire.
To learn more on Pythagorean theorem: https://brainly.com/question/26183488
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