Based on the calculations, the initial points of vector (v) are represented by: D. (-5, -3).
Let (x, y) be the initial point of the given vector. Thus, the magnitude of the vector (v) can be written by using the distance formula as follows:
Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]
|v| = √[(-1 - x)² + (-6 - y)²]
Substituting the magnitude of v, we have:
5 = √[(-1 - x)² + (-6 - y)²]
25 = (-1 - x)² + (-6 - y)²
25 = (-1 - (-5))² + (-6 - (-3))²
25 = (-1 + 5)² + (-6 + 3)²
25 = 4² + -3²
25 = 16 + 9
25 = 25.
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