Final answer:
The magnitude of the vector PQ, where P is <-4,-10> and Q is <-5,2>, can be calculated using the distance formula derived from Pythagoras' theorem. The calculation yields a magnitude of √145 or approximately 12.04.
Step-by-step explanation:
The question asks to find the magnitude of the vector PQ. To achieve this, we need to find the distance between points P and Q. This involves applying the formula derived from Pythagoras' theorem for calculating the distance between two points in a plane, which is defined by √((x₂-x₁)² + (y₂-y₁)²). In this case, P corresponds to x₁ and y₁, while Q corresponds to x₂ and y₂. Thus, the calculation is √((-5 - (-4))² + (2 - (-10))²), which simplifies to √(1² + 12²) = √145. So the magnitude of the vector PQ is √145 or approximately 12.04.
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