Question

A small craft in lake Ontario sends out a distances signal. The coordinates of the boat in trouble are (57,64). One rescue boat is at the coordinates (67,83) and a second coast guard craft is at coordinates (65,46). Assuming both rescue crafts travel at the same rate, which one get to the distressed boat the fastest?

Answer 1

Answer:

The coast guard craft will get to the distressed boat the fastest.

Step-by-step explanation:

The coordinates of boat are (57,64).

The coordinates of rescue boat are (67,83).

The  coordinates of coast guard craft are (65,46).

Both rescue crafts travel at the same rate. One of them will get to the distressed boat the faster, whose distance from the boat is least.

Distance formula:

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

The distance between boat and rescue boat is

$d_1=\sqrt{(67-57)^2+(83-64)^2}=21.4709105536\approx 21.47$

The distance between boat and coast guard craft is

$d_2=\sqrt{(65-57)^2+(46-64)^2}=19.6977156036\approx 19.70$

Since the distance between boat and coast guard craft is least, therefore coast guard craft will get to the distressed boat the fastest.