Translation Matrix

How to use the translation matrix to find the image under a translation: formula, 1 example, and its solution.

Formula

Formula

For the translation (x, y) → (x + a, y + b),
the translation matrix is
+[a / b].

Example

Example

Solution

Write the vertex matrix.
Write the vertices in each column.

A(-2, 1), B(2, 3), C(0, -1)

So the vertex matrix is
[-2 2 0 / 1 3 -1].

The image is under the translation
(x, y) → (x + 7, y + 5).

So add the translation matrix.

+[7 7 7 / 5 5 5]

So the vertex matrix of the image is
[-2 2 0 / 1 3 -1] + [7 7 7 / 5 5 5].

Add the matrices.

Row 1, Column 1:
-2 + 7 = 5

Row 1, Column 2:
2 + 7 = 9

Row 1, Column 3:
0 + 7 = 7

Row 2, Column 1:
1 + 5 = 6

Row 2, Column 2:
3 + 5 = 8

Row 2, Column 3:
-1 + 5 = 4

So [5 9 7 / 6 8 4]
is the vertex matrix of the image.

So column 1 is the image of A:
A'(5, 6).

Column 2 is the image of B:
B'(9, 8).

Column 3 is the image of C:
C'(7, 4).

So
A'(5, 6)
B'(9, 8)
C'(7, 4)
is the answer.

Graph

This is the graph of △ABC
and its image △A'B'C'.

The image is under the translation
(x, y) → (x + 7, y + 5).