# Exploring Translations in the Coordinate Plane

- Author:
- Tim Brzezinski

- Topic:
- Coordinates, Geometry, Translation, Vectors

## Interact with the app below for a few minutes. Move LARGE POINTS around and drag Lisa's picture. Explore!

In the app above, what do you notice? What do you wonder? Notice anything interesting? List anything you observe or that you found interesting:

In the app below:
Position Mona so that and .
Position vector ** u **so that .
What are the coordinates of ? What are the coordinates of ?

In the app below:
Position Mona so that and .
Position vector ** u **so that .
What are the coordinates of ? What are the coordinates of ?

Use the app below to help answer the following question:
**What vector u = <? , ?> **places Lisa's image right on top of her original pic (preimage)?

Use the apps below to help answer the following question:

**What vector u**moves Lisa 5 units to the right?**What vector u**moves Lisa 3 units down?**What vector u**moves Lisa 5 units to the right AND 3 units down?

Suppose *u* = <a, b> and suppose . What would the coordinates of be if point is translated by **vector u**?

Suppose *u* = <a,b> and suppose . What would the coordinates of be if point is translated by **vector u**? Write in terms of

*x,*

*y, a*, and

*b*.