Exploring Translations in the Coordinate Plane

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.