Question

Point A is located at (4, 7). It will be translated 5 units right and 3 units down. Write the rule and give the location of point A.

Answer 1

The rule of translation is
`A(x',y') = A(x,y) + (5,-3)`.

The translated vector is
`A(x',y') = (9, 4)`.

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:

`A(x',y') = A(x,y) + U(x,y)` (Eq. 1)

Where:

`A(x,y)` - Original vector, dimensionless.

`U(x,y)` - Translation vector, dimensionless.

`A(x',y')` - Translated vector, dimensionless.

If we know that
`U(x, y) = (5, -3)`, then the rule of translation is described by:

`A(x',y') = A(x,y) + (5,-3)` (Eq. 2)

If
`A(x, y) = (4,7)`, then the new location of A is:

`A(x',y') = (4,7)+(5,-3)`

`A(x',y') = (9, 4)`

The translated vector is
`A(x',y') = (9, 4)`.