Question

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

Make sure to explain how you go this answer, please

Answer 1

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

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)`.