Question

Given the translation T(3, -1), translate the ordered pairs (-3, 6) and (9, -8). choices: (0, 7) and (6, -7) (0, 5) and (12, -9) (0, 4) and (6, 10) (-6, 5) and (12, -9)

Answer 1

The translated ordered pairs are
`P_(1)'(x,y) = (0, 5)` and
`P_(2)' (x,y) = (12, -9)`.

Explanation:

Vectorially speaking, a translation is defined by the following formula:

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

Where:

`P(x,y)` - Original point.

`P'(x,y)` - Translated point.

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

If we know that
`P_(1)(x,y) = (-3, 6)`,
`P_(2) (x,y) = (9, -8)` and
`T(x,y) = (3, -1)`, then the translated points are, respectively:

`P_(1)'(x,y) = (-3, 6) + (3,-1)`

`P_(1)'(x,y) = (0, 5)`

`P'_(2)(x,y) = (9,-8) + (3, -1)`

`P_(2)' (x,y) = (12, -9)`

The translated ordered pairs are
`P_(1)'(x,y) = (0, 5)` and
`P_(2)' (x,y) = (12, -9)`.