Question

Find the magnitude of the vector PQ→ when P = (-1, -4) and Q = (3, -9). Round to the nearest hundredth.

A) 5.00
B) 6.40
C) 7.81
D) 9.22

Answer 1

The magnitude of the vector PQ when P = (-1, -4) and Q = (3, -9) is approximately 6.40 (B).

Step-by-step explanation:

To find the magnitude of the vector PQ, we use the distance formula, which is derived from the Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:

`\[ d = sqrt((x2 - x1)^2 + (y2 - y1)^2) \]`

In this case, P = (-1, -4) and Q = (3, -9). Substituting the coordinates into the formula:

`\[ d = sqrt((3 - (-1))^2 + ((-9) - (-4))^2) \]`

`\[ d = sqrt(4^2 + (-5)^2) \]`

`\[ d = sqrt(16 + 25) \]`

`\[ d = sqrt(41) ≈ 6.40 \]`

Therefore, the magnitude of the vector PQ is approximately (B)6.40, rounded to the nearest hundredth. This corresponds to option B in the given choices.

Understanding vector magnitudes is crucial in physics, engineering, and various mathematical applications, as it represents the length or size of a vector in a multi-dimensional space.