# Translation: Point

How to find the image under the translation of a point: formula, 2 examples, and their solutions.

## Formula

The image of a point (x, y)

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

(x + a, y + b).

## Example(3, 1), Translation (x, y) → (x + 4, y + 5)

Solution

Solution (Detail)

The image of (3, 1) is

under the translation (x, y) → (x + 4, y + 5).

Then the image point is

(3 + 4, 1 + 5).

3 + 4 = 7

1 + 5 = 6

So (7, 6) is the answer.

Graph

This is the graph of (3, 1)

and its image

under the translation (x, y) → (x + 4, y + 5):

(3 + 4, 1 + 5).

## Example(8, -1), Translation (x, y) → (x - 7, y + 3)

Solution

Solution (Detail)

The image of (8, -1) is

under the translation (x, y) → (x - 7, y + 3).

Then the image point is

(8 - 7, -1 + 3).

8 - 7 = 1

-1 + 3 = 2

So (1, 2) is the answer.

Graph

This is the graph of (8, -1)

and its image

under the translation (x, y) → (x - 7, y + 3):

(8 - 7, -1 + 3).