Question

Write a translation rule that maps point D(7, −3) onto point D'(2, 5).

Answer 1

Answer:

The translation rule is described by $D'(x,y) =(x-5,y+8)$.

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:

$D'(x,y) = D(x,y) +U(x,y)$ (Eq. 1)

Where:

$D(x,y)$ - Original vector with respect to origin, dimensionless.

$D'(x,y)$ - Translated vector with respect to origin, dimensionless.

$U(x,y)$ - Translation vector with respect to original vector, dimensionless.

From (Eq. 1) we get that translation vector is:

$U(x,y) = D'(x,y)-D(x,y)$

If we know that $D(x,y) = (7,-3)$ and $D'(x,y) =(2,5)$, then the translation vector is:

$U(x,y) = (2,5)-(7,-3)$

$U(x,y) = (-5,8)$

And we find the translation rule by assuming that $D(x,y) = (x,y)$ and $U(x,y) = (-5,8)$ in (Eq. 1):

$D'(x,y) = (x,y)+(-5,8)$

$D'(x,y) =(x-5,y+8)$

The translation rule is described by $D'(x,y) =(x-5,y+8)$.