Question

This is my first question ever on open study since i just made the account :)

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. Which theorem or postulate does this demonstrate? You must show all work and steps in order to receive credit.

A coordinate graph shows two points labeled 1,5 with an arrow pointing SE and 4,1 with an arrow pointing N.

Answer 1

To find the location of the distress boat, we need to find where the signals intersect.

Pretend that the SE signal just means a 45 degree slope through it's partner point

And let the N signal mean that it is a verticle like going though it's partner point.

At what point do the two lines intersect when graphed?

Answer 2

For ship 1 the equation of the line (signal ray) is x = 4 ---------------(1)
and for the ship 2 the line equation is
y = -tan45 * x + 6 = -x+6 (slope-intercept form) ------------------------(2)
The intersection is (substitute x = 4 in the second equation giving y = -4 + 6 = 2
Therefore the coordinates of the ship in distress = (4,2)
I hope this helps