Question

50 points! pls help geometry

Ship A receives a distress signal from the north, and ship B receives a distress signal from the same vessel from the southeast. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences. You must show all work in order to receive credit.

Answer 1

the answer is 4,2

Answer 2

The location of the vessel of distress is (4,2).

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,

`y-5=-1(x-1)`

`y+x=6`

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).