Question

A point travels East 3 spaces and South 8 spaces.Write the description in algebraic terms.

Answer 1

A point travels East 3 spaces and South 8 spaces.

Algebraic equation

`P'(x,y) = (x+3, y-8)`

Explanation:

From the viewpoint of Linear Algebra, the description can be described by means of translation, which is defined as:

`P'(x,y) =P(x,y) +T(x,y)` (1)

Where:

`P(x,y)` - Initial position of the traveller, dimensionless.

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

`P'(x,y)` - Final position of the traveller, dimensionless.

Let suppose that
`y > 0` represents the number of steps to the north, and
`x> 0`, the number of steps to the east.

If we know that
`P(x,y) =(x,y)` and
`T(x,y) = (3, -8)`, then the resulting equation is:

`P'(x,y) = (x,y) +(3,-8)`

`P'(x,y) = (x+3, y-8)`