Answer:
The location of the vessel of distress is (4,2).
Step-by-step explanation:
Suppose point P represents the location of the vessel in distress,
Given,
Ship A receives a distress signal from the north,
A vertical line must be join the point P and A,
By the given diagram,
The equation of that line is x = 4,
Now, ship B receives a distress signal from the same vessel from the southeast.
We know that a southeast line makes the angle 315° with the positive x-axis,
Equation that passes through both B and P having the slope -1, ( slope = tan Ф, where Ф is the angle with positive x-axis )
Now, the equation of a line having slope -1 and passes through (1,5) is,
[tex]y-5=-1(x-1)[/tex]
[tex]y+x=6[/tex]
Thus, the points B and P are joined by the line y + x = 6
Line x = 4 and y + x = 6 must intersect at P,
By solving these equations,
We get, x=4 and y = 2,
⇒ Coordinates of P are (4,2)
Therefore, the location of the vessel of distress is (4,2).
