We are given a diagram and want to know if the blue figure is a translation of the red figure. Let's take a look at the diagram.

Recall that a translation is a transformation that involves sliding a figure without turning, rotating, or changing its size. Let's see if the red figure can slide to form the blue figure.

From the diagram, we can see that the red figure slides to form the blue one. Therefore, the blue figure is a translation of the red figure.

Extra

Translations in a Coordinate Plane

To translate a figure

a

units horizontally and

b

units vertically in a coordinate plane, we need to add

a

to the

x -

coordinates and

b

to the

y -

coordinates of all of their vertices.

(x, y) \to (x + a, y + b)

For example, to translate the red triangle in the graph to form a blue triangle, we need to translate it

4

units to the right and

1

unit down.

Let's see how the coordinates of the vertices change!

Initial Position $(x, y)$	$(x + 4, y - 1)$	New Position
$(- 4, 3)$	$(- 4 + 4, 3 - 1)$	$(0, 2)$
$(- 2, 1)$	$(- 2 + 4, 1 - 1)$	$(2, 0)$
$(- 1, 2)$	$(- 1 + 4, 2 - 1)$	$(3, 1)$

Exercise