Question

If A has coordinates (0,4) and B has coordinates (-2,-9), then AB is given byA. <2,-13>B. <2,13>C. <-2,-13>D. <-2,13>

Answer 1

To obtain the coordinates of the vector AB, the following steps are necessary:

Step 1: Recall the expression for the resultant AB of two vectors A and B, as follows:

`\begin{gathered} \text{Given the vectors A, and B},\text{ AB is as :} \\ \vec{AB}=\vec{B}-\vec{A} \\ \text{If:} \\ \vec{A}=(a_1,a_2) \\ \vec{B}=(b_1,b_2) \\ \text{Thus:} \\ \vec{AB}=\vec{B}-\vec{A}=(b_1,b_2)-(a_1,a_2)=(b_1-a_1,b_2-a_2) \end{gathered}`

Step 2: Apply the expression to solve the question, as follows:

`\begin{gathered} Given\text{ that:} \\ \vec{A}=(0_{},4_{}) \\ \vec{B}=(-2,-9) \\ \text{Thus:} \\ \vec{AB}=\vec{B}-\vec{A}=(-2_{},-9_{})-(0_{},4)=(-2_{}-0_{},-9_{}-4_{})=(-2,-13) \end{gathered}`

Thus, the answer is (-2, -13) (option C)