# Translation of a Point

How to find the point under the given translation: formula, example, and its solution.

## Formula

The image of a point (*x*, *y*)

under the translation (*x*, *y*) → (*x* + *a*, *y* + *b*)

is (*x* + *a*, *y* + *b*).

Unlike the translation of a function,

write +*a* and +*b*.

Translation of a function

## Example

The translation is (*x*, *y*) → (*x* [+ 7], *y* [+ 5]).

The image of *A*(-2, 1) is*A*'(-2 [+ 7], 1 [+ 5])

= (5, 6).

The image of *B*(2, 3) is*B*'(2 [+ 7], 3 [+ 5])

= (9, 8).

The image of *C*(0, -1) is*C*'(0 [+ 7], -1 [+ 5])

= (7, 4).

△*ABC* has vertices*A*(-2, 1), *B*(2, 3), and *C*(0, -1).

△*A'B'C'* has vertices*A*'(5, 6), *B*'(9, 8), and *C*'(7, 4).

Use these vertices

to draw △*ABC* and its image △*A'B'C'*

on the coordinate plane.

As you can see,

△*A'B'C'* is under the translation

(*x*, *y*) → (*x* [+ 7], *y* [+ 5]).

The triangle is only moved.

There's no change in its size.

So, under a translation,

the length and the area are reserved.