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 mouse's displacement.(1 point)
To find the mouse's displacement, we need to calculate the distance and direction from its initial position to its final position.
As given, the mouse initially moves 41 cm south. This means it moves downward on the y-axis by 41 cm.
Next, the mouse takes a 90-degree turn and moves 64 cm west. This means it moves leftward on the x-axis by 64 cm.
We can use these two displacements to form a right-angled triangle. The mouse's displacement will be the hypotenuse of this triangle.
Using the Pythagorean theorem, we can find the magnitude of the displacement:
displacement^2 = (41 cm)^2 + (64 cm)^2
displacement^2 = 1681 cm^2 + 4096 cm^2
displacement^2 = 5777 cm^2
displacement ≈ √5777 cm
displacement ≈ 76.01 cm
Therefore, the mouse's displacement is approximately 76.01 cm.