Final answer:
The magnitude of vector ⇒PQ is found by using the distance formula. After plugging in the coordinates for points P and Q, the magnitude is determined to be approximately 7.28, which does not match the provided choices, indicating a possible typo in the options.
Step-by-step explanation:
To find the magnitude of the vector ⇒PQ when P = (-1, -3) and Q = (1, 4), we can use the distance formula applied to vectors, which is derived from the Pythagorean theorem. The formula for the magnitude of a vector from point P(x1, y1) to point Q(x2, y2) is:
|PQ| = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of P and Q, we get:
|PQ| = √[(1 - (-1))^2 + (4 - (-3))^2]
|PQ| = √[(1 + 1)^2 + (4 + 3)^2]
|PQ| = √[2^2 + 7^2]
|PQ| = √[4 + 49]
|PQ| = √[53]
To the nearest hundredth, the magnitude is approximately:
|PQ| = 7.28
Since none of the given options match this result, it seems there could be a typo in the provided options.