Final answer:
The vector in component form is (-7, -1) with a magnitude of 7.07, matching option C. The component form is determined by subtracting the initial point coordinates from the terminal point coordinates and the magnitude is calculated via the Pythagorean theorem.
Step-by-step explanation:
To write the vector in component form, you subtract the coordinates of the initial point from the coordinates of the terminal point. The component form is given by (Δx, Δy), where Δx = x2 − x1 and Δy = y2 − y1. For the given points (11, -4) as the initial and (4, -5) as the terminal point, the component form would be (4 − 11, -5 - (-4)) or (-7, -1).
To find the magnitude, use the Pythagorean theorem, which is the square root of the sum of the squares of the x and y components. So, the magnitude is √((-7)^2 + (-1)^2) = √(49 + 1) = √(50), which simplifies to approximately 7.07. Therefore, the correct option is C. Component Form: (-7, -1); Magnitude: 7.07.