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Multiple Choice
A cyclist travels km east and then km north. What is the straight-line distance from the starting point to the cyclist's final position?
A
km
B
km
C
km
D
km
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Verified step by step guidance
1
Identify the problem as finding the straight-line distance (displacement) between the starting point and the final position of the cyclist after traveling east and then north.
Recognize that the cyclist's path forms a right-angled triangle, where the legs are the distances traveled east and north, and the hypotenuse is the straight-line distance we need to find.
Use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse \(c\) is equal to the sum of the squares of the other two sides \(a\) and \(b\): \(c^2 = a^2 + b^2\).
Substitute the given distances into the formula: let \(a = 3\) km (east) and \(b = 4\) km (north), so \(c^2 = (3)^2 + (4)^2\).
Solve for \(c\) by taking the square root of both sides: \(c = \sqrt{(3)^2 + (4)^2}\), which gives the straight-line distance from the starting point to the final position.