Question

a mouse in a maze scurries 41 cm south and then takes a 90 - degree turn and scurries 64 cm west to get a piece of cheese. find the mouses displacement. (1 point)
76 cm southwest
105 cm
southwest
zero

Explanation:

Step1: Use Pythagorean theorem

The two displacements (south and west) are perpendicular. Let \(a = 41\) cm (south - direction 1) and \(b=64\) cm (west - direction 2). The displacement \(d\) is the hypotenuse of a right - triangle. The Pythagorean theorem is \(d=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 41\) and \(b = 64\) into the formula: \(d=\sqrt{41^{2}+64^{2}}=\sqrt{1681 + 4096}=\sqrt{5777}\).
Calculate \(\sqrt{5777}\approx76\) cm.
Since the two directions (south and west) are perpendicular, the direction of the displacement is southwest.

Answer:

76 cm southwest