Questions: 1. Express (X Y) as an ordered pair if the coordinates of the points are X(1,2) and Y(4,5). A. [3,3] B. 3 C. 4.2 D. 9 2. Find the component form of the vector (A B) with initial point A(3,5) and terminal point B(1,2). A. <-2,-3> B. <2,3> C. <4,7> D. <3,10>

1. Express (X Y) as an ordered pair if the coordinates of the points are X(1,2) and Y(4,5).
A. [3,3]
B. 3
C. 4.2
D. 9

2. Find the component form of the vector (A B) with initial point A(3,5) and terminal point B(1,2).
A. <-2,-3>
B. <2,3>
C. <4,7>
D. <3,10>

Transcript text: 1. Express $\overrightarrow{X Y}$ as an ordered pair if the coordinates of the points are $X(1,2)$ and $Y(4,5)$. A. $[3,3]$ B. 3 C. 4.2 D. 9 2. Find the component form of the vector $\overrightarrow{A B}$ with initial point $A(3,5)$ and terminal point $B(1,2)$. A. $\langle-2,-3\rangle$ B. $\langle 2,3\rangle$ C. $\langle 4,7\rangle$ D. $\langle 3,10\rangle$

Solution

Solution Steps

To express $\overrightarrow{XY}$ as an ordered pair, subtract the coordinates of point $X$ from the coordinates of point $Y$.
To find the component form of the vector $\overrightarrow{AB}$, subtract the coordinates of point $A$ from the coordinates of point $B$.

Step 1: Calculate $\overrightarrow{XY}$

To express $\overrightarrow{XY}$ as an ordered pair, we subtract the coordinates of point $X(1, 2)$ from the coordinates of point $Y(4, 5)$:

\[ \overrightarrow{XY} = (4 - 1, 5 - 2) = (3, 3) \]

Step 2: Calculate $\overrightarrow{AB}$

To find the component form of the vector $\overrightarrow{AB}$ with initial point $A(3, 5)$ and terminal point $B(1, 2)$, we subtract the coordinates of point $A$ from the coordinates of point $B$:

\[ \overrightarrow{AB} = (1 - 3, 2 - 5) = (-2, -3) \]