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

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

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!