Answer:
The rule of translation is [tex]A(x',y') = A(x,y) + (5,-3)[/tex].
The translated vector is [tex]A(x',y') = (9, 4)[/tex].
Step-by-step explanation:
Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.
We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:
[tex]A(x',y') = A(x,y) + U(x,y)[/tex] (Eq. 1)
Where:
[tex]A(x,y)[/tex] - Original vector, dimensionless.
[tex]U(x,y)[/tex] - Translation vector, dimensionless.
[tex]A(x',y')[/tex] - Translated vector, dimensionless.
If we know that [tex]U(x, y) = (5, -3)[/tex], then the rule of translation is described by:
[tex]A(x',y') = A(x,y) + (5,-3)[/tex] (Eq. 2)
If [tex]A(x, y) = (4,7)[/tex], then the new location of A is:
[tex]A(x',y') = (4,7)+(5,-3)[/tex]
[tex]A(x',y') = (9, 4)[/tex]
The translated vector is [tex]A(x',y') = (9, 4)[/tex].
