To find the vector that goes from the initial point [tex]\((4,0)\)[/tex] to the final point [tex]\((1,-3)\)[/tex], follow these steps:
1. Identify the coordinates of the points:
- The initial point [tex]\(P_1\)[/tex] has coordinates [tex]\((x_1, y_1) = (4, 0)\)[/tex].
- The final point [tex]\(P_2\)[/tex] has coordinates [tex]\((x_2, y_2) = (1, -3)\)[/tex].
2. Calculate the components of the vector:
- The change in the x-coordinate (horizontal change) is given by [tex]\(\Delta x = x_2 - x_1\)[/tex].
- The change in the y-coordinate (vertical change) is given by [tex]\(\Delta y = y_2 - y_1\)[/tex].
3. Perform the subtractions:
- For the x-component: [tex]\(1 - 4 = -3\)[/tex].
- For the y-component: [tex]\(-3 - 0 = -3\)[/tex].
4. Combine the components into a vector:
- The vector that goes from [tex]\(P_1\)[/tex] to [tex]\(P_2\)[/tex] is [tex]\((-3, -3\)[/tex]).
Thus, the vector that goes from [tex]\((4,0)\)[/tex] to [tex]\((1,-3)\)[/tex] is given by [tex]\((-3, -3)\)[/tex].
Without additional context or labeled options, like [tex]\( a, b, c, d\)[/tex], it is not possible to select one of the given options. But we have found that the vector is [tex]\((-3, -3)\)[/tex].
