Question

which vector below goes from (0, 0) to (-4, 2)?

Explanation:

Step1: Analyze the coordinates

The vector from \((0,0)\) to \((-4,2)\) has an \(x\) - component of \(-4\) (left direction) and a \(y\) - component of \(2\) (up direction).

Step2: Check each vector

• Vector \(\vec{a}\): It has a negative \(x\) - component and a small positive \(y\) - component. But its \(y\) - component is not large enough compared to the required \(y = 2\).
• Vector \(\vec{b}\): It has a positive \(x\) - component, which is not what we need (\(x=-4<0\)).
• Vector \(\vec{d}\): It has a positive \(x\) - component (since it goes to the right in the \(x\) - direction) and a negative \(y\) - component (since it goes down in the \(y\) - direction).
• Vector \(\vec{c}\): It has a negative \(x\) - component (moves to the left) and a positive \(y\) - component (moves up), which matches the direction from \((0,0)\) to \((-4,2)\).

Answer:

D. \(\vec{c}\)