Answer:
Component form of the vector will be (-1, 2).
Step-by-step explanation:
When [tex]P(x_1, y_1)[/tex] translates to [tex]P'(x_2,y_2)[/tex] vector V formed after the translation will be,
V = [tex]<(x_2-x_1), (y_2-y_1)>[/tex]
If we draw this vector on a graph,
Vector will start from origin and the terminal point will be at [tex][(x_2-x_1), (y_2-y_1)][/tex]
Therefore, component form of the vector that translates from P(-3, 6) and P'(-4, 8) will be,
V = [tex]<(-4+3),(8-6)>[/tex]
V = [tex]<(-1,2)>[/tex]
Translation involves changing the position of a point
The vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
The points are given as:
[tex]\mathbf{P = (-3,6)}[/tex]
[tex]\mathbf{P' = (-4,8)}[/tex]
The translation rule is calculated as:
[tex]\mathbf{(x,y) = P' - P}[/tex]
So, we have:
[tex]\mathbf{(x,y) = (-4,8) - (-3,6)}[/tex]
Combine
[tex]\mathbf{(x,y) = (-4+3,8-6)}[/tex]
[tex]\mathbf{(x,y) = (-1,2)}[/tex]
Express as vectors
[tex]\mathbf{<x,y> = <-1,2>}[/tex]
Hence, the vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
Read more about translations at:
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