To determine which vector goes from [tex]\((0,0)\)[/tex] to [tex]\((1,-3)\)[/tex], let's analyze the movement from the starting point to the endpoint.
1. Starting Point & Endpoint: We're moving from the initial point [tex]\((0,0)\)[/tex] to the final point [tex]\((1,-3)\)[/tex].
2. Calculating the Vector Components:
- The change in the [tex]\(x\)[/tex]-coordinate is [tex]\(1 - 0 = 1\)[/tex].
- The change in the [tex]\(y\)[/tex]-coordinate is [tex]\(-3 - 0 = -3\)[/tex].
So, the vector that describes this movement is [tex]\(\vec{v} = (1, -3)\)[/tex].
Given the options:
- A. [tex]\(\vec{c}\)[/tex]
- B. [tex]\(d\)[/tex]
- C. [tex]\(b\)[/tex]
- D. [tex]\(\vec{a}\)[/tex]
We need to identify which option represents the vector [tex]\((1, -3)\)[/tex].
From the information provided, the correct answer is option A, [tex]\(\vec{c}\)[/tex].
Thus, the vector [tex]\( \vec{c} \)[/tex] goes from [tex]\((0,0)\)[/tex] to [tex]\((1,-3)\)[/tex]. Therefore, the answer is:
A. [tex]\(\vec{c}\)[/tex]
