To determine which vector goes from the point [tex]\((1,1)\)[/tex] to the point [tex]\((0,2)\)[/tex], we need to calculate the resulting vector from these two points.
1. Calculate the vector components:
- The x-component of the vector is found by subtracting the x-coordinate of the first point from the x-coordinate of the second point:
[tex]\[
0 - 1 = -1
\][/tex]
- The y-component of the vector is found by subtracting the y-coordinate of the first point from the y-coordinate of the second point:
[tex]\[
2 - 1 = 1
\][/tex]
- Thus, the vector that goes from [tex]\((1,1)\)[/tex] to [tex]\((0,2)\)[/tex] is:
[tex]\[
(-1, 1)
\][/tex]
2. Match this vector to the options given:
- Option A: [tex]\(a = (-1, 1)\)[/tex]
- Option B: [tex]\(d = (0, 1)\)[/tex]
- Option C: [tex]\(b = (-1, 2)\)[/tex]
- Option D: [tex]\(C = (0, 2)\)[/tex]
By comparing our calculated vector [tex]\((-1, 1)\)[/tex] with the options provided, we observe that it matches option A.
Therefore, the vector that goes from [tex]\((1,1)\)[/tex] to [tex]\((0,2)\)[/tex] is [tex]\(\mathbf{a}\)[/tex].
