Examples:
1) Find the distance between the points (2, 4) and (1, -1).
Solution:
The square of the distance is equal to:
(1-2)2 + (-1-4)2 = 26
Hence, the distance is equal to sqrt(26).
2) A cruise ship leaves a port heading due east at a constant speed of 5 miles per hour (mph). At exactly noon, the cruise ship is 5 miles due south of a cabin cruiser that is moving south at a constant speed of 10 mph. Express the distance d between the ships, as a function of time t.
Solution:
First, draw a picture describing what is happening at different stages.
After a time t (in hours) has passes, the cruise ship has moved east 5t miles,
and the cabin cruiser has moved south 10t miles, as depicted in diagram (a).
Diagram (b) shows the relative position of each ship after t hours. The right
triangle extracted from (b) is shown in (c). By the Pythagorean Theorem, the
square of the distance d between the ships after time t is:
d2 = (5 - 10t)2 + (5t)2
d2 = 125t2 - 100t + 25
Thus, d = sqrt(125t2 - 100t + 25)
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