Answer:
The translation rule is described by [tex]D'(x,y) =(x-5,y+8)[/tex].
Step-by-step explanation:
According to Linear Algebra, a translation consists in sum a given vector (original point in this case) with another vector (translation vector). We can define translation as follows:
[tex]D'(x,y) = D(x,y) +U(x,y)[/tex] (Eq. 1)
Where:
[tex]D(x,y)[/tex] - Original vector with respect to origin, dimensionless.
[tex]D'(x,y)[/tex] - Translated vector with respect to origin, dimensionless.
[tex]U(x,y)[/tex] - Translation vector with respect to original vector, dimensionless.
From (Eq. 1) we get that translation vector is:
[tex]U(x,y) = D'(x,y)-D(x,y)[/tex]
If we know that [tex]D(x,y) = (7,-3)[/tex] and [tex]D'(x,y) =(2,5)[/tex], then the translation vector is:
[tex]U(x,y) = (2,5)-(7,-3)[/tex]
[tex]U(x,y) = (-5,8)[/tex]
And we find the translation rule by assuming that [tex]D(x,y) = (x,y)[/tex] and [tex]U(x,y) = (-5,8)[/tex] in (Eq. 1):
[tex]D'(x,y) = (x,y)+(-5,8)[/tex]
[tex]D'(x,y) =(x-5,y+8)[/tex]
The translation rule is described by [tex]D'(x,y) =(x-5,y+8)[/tex].
