Question

A vector is used to express a car's change in position, or displacement, by tracking its motion over a large area defined by a coordinate grid. If the car begins at (−3,−5) and ends at (5,9), which of these expresses the car's displacement in vector form?
A
(14,8)

B
(10,12)

C
(8,14)

D
(2,4)

Answer 1

Answer:

The correct answer is option C: (8, 14).

Step-by-step explanation:

The car's displacement in vector form can be found by subtracting the initial points from the final points.    

Initial: (x₁, y₁) = (-3, -5)

Final: (x₂, y₂) = (5, 9)          

For the x-coordinate, we have:  

$d_{x} = x_{2} - x_{1} = 5 - (-3) = 8$

And for the y-coordinate, we have:

$d_{y} = y_{2} - y_{1} = 9 - (-5) = 14$

The car's displacement in vector form is:

$d = (d_{x}, d_{y}) = (8, 14)$  

Therefore, the correct answer is option C: (8, 14).

I hope it helps you!