Final answer:
The magnitude of the vector extending from the origin to (-5.0cm, 8.0cm) is 9.43 cm, using the Pythagorean theorem to calculate the length of the vector.
Step-by-step explanation:
To find the magnitude of a vector that extends from the origin to (-5.0cm, 8.0 cm), we can utilize the Pythagorean theorem which applies to the vector components treated as sides of a right-angled triangle. The magnitude (also known as the length) of the vector is calculated using the formula: magnitude = √(x² + y²), where 'x' and 'y' are the horizontal and vertical components of the vector, respectively.
In this case, x is -5.0 cm and y is 8.0 cm. Therefore, the magnitude is:
magnitude = √((-5.0 cm)² + (8.0 cm)²)
magnitude = √(25.0 cm² + 64.0 cm²)
magnitude = √(89.0 cm²)
magnitude = 9.43 cm (to two decimal places)
The magnitude of the vector is thus 9.43 cm, rounding to the nearest hundredth for precision.