Translation: Point

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

Formula

Formula

The image of a point (x, y)
under the translation (x, y) → (x + a, y + b) is
(x + a, y + b).

Example 1

Example

Solution

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 2

Example

Solution

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).