Answer:
7.1 units
Explanation:
You want to know the distance from point (40, 10) to the line segment between points (-20, 60) and (50, -10).
Equation of the line
The line representing the path of travel of the ship can be written using the form ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
Filling in the coordinate values for the end points of the ship's path, we have ...
(-10 -60)(x -(-20)) -(50 -(-20))(y -60) = 0
-70(x +20) -70(y -60) = 0 . . . . simplify a bit
x + y -40 = 0 . . . . . . . . . . divide by -70, write in general form
Distance to the line
The distance from (x, y) to line ax+by+c=0 is given by the formula ...
d = |ax +by +c|/√(a²+b²)
For the line above, this is ...
d = |x +y -40|/√(1+1) = |x +y +40|/√2
Then the distance from point (40, 10) is ...
d = |40 +10 -40|/√2 = 10/√2 = 5√2
d ≈ 7.1
The ship will come as close as 7.1 units from the iceberg.
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Additional comment
The units used for the coordinates are not given by this problem. They could be miles, kilometers, furlongs, nautical miles, or something else. We don't know. All we can say is that the distance of closest approach is 7.1 of those map units, whatever they are.