To translate a shape means to move it without changing its size or how it looks. We can use something called vectors to show this movement. Vectors tell us both the direction to move and how far to go.

Here’s How to Do a Translation:

1. Identify the Shape: Let's say we have a triangle. Its points are A(1, 2), B(3, 4), and C(5, 1).

2. Choose the Vector: We need a translation vector. Let’s pick $\mathbf{v} = (2, 3)$. This means we will move each point 2 units to the right and 3 units up.

3. Move Each Point:

   • For Point A(1, 2):
     • New Point A' = $(1 + 2, 2 + 3) = (3, 5)$
   • For Point B(3, 4):
     • New Point B' = $(3 + 2, 4 + 3) = (5, 7)$
   • For Point C(5, 1):
     • New Point C' = $(5 + 2, 1 + 3) = (7, 4)$

Results:

Now, your new triangle points are A'(3, 5), B'(5, 7), and C'(7, 4). Using vectors makes it easier to see how the shape moves!