Question

the component form of a vector indicates the changes in x and y from the starting point to the endpoint. what is the component form of this vector? a (2,0) b (-4,5) c (5,2) d (2,-5)

Explanation:

Step1: Identify the start and end points

The starting point of the vector is $(2, 5)$ and the endpoint is $(4, 0)$.

Step2: Calculate the change in x (Δx)

The change in x is found by subtracting the x - coordinate of the start point from the x - coordinate of the end point. So, $\Delta x=4 - 2=2$.

Step3: Calculate the change in y (Δy)

The change in y is found by subtracting the y - coordinate of the start point from the y - coordinate of the end point. So, $\Delta y = 0-5=- 5$.

Step4: Write the component form

The component form of a vector is $\langle\Delta x,\Delta y
angle$. Substituting the values of $\Delta x$ and $\Delta y$ we found, the component form of the vector is $\langle2,-5
angle$.

Answer:

D. $\langle 2, -5
angle$