Ship A receives a distress signal from the east and ship B receives a distress signal from the same vessel from the northwest. At what location is the vessel in distress located
II can’t read the coordinates of A and B ( I cant justify the answer 4,2), so I’ll offer a general solution
Let’s assume we know the coordinates of the ships’ positions A(xa,ya) and B(xb,yb) and let the position of the ship in distress be (unknown) C(xc,yc). We deduce that ;
1. xc is greater than xa (to the right = east = greater x),
2. yc is the same as ya because an eastward direction lies on a line parallel to the x axis,
3. xa and xc are both less than xb (both to the left), since the NW direction lies on a line that
is at an angle of 135 degrees to the positive direction of the x axis. In other words, both A and C are left of and above B. Using the same logic, ya (=yc) is greater than yb (north =above)
4. NW implies an angle of 45 degrees, so we construct a square whose bottom right point is B, whose sides are parallel to the axes. The length of its sides are (ya -yb). The ship in distress © is going to be on the end of the diagonal that contains B.
5. The coordinates of the ship in distress are (xb-ya+yb , ya)
And yes, the postulate is that two different lines of the same plane are either parallel or intersect in one point.