# Translations on Coordinate Plane

Author:
egunn
Drag the TranslationVector around until you understand how the sketch works. When the Image is to the right of the Preimage, what can you say about the TranslationVector? What is positive, what is negative, what is zero? When the Image is to the left of the Preimage, what can you say about the TranslationVector? When the Image is above the Preimage, what can you say about the TranslationVector? When the Image is below the Preimage, what can you say about the TranslationVector? When the Image is above and to the right of the Preimage, what can you say about the TranslationVector? When the Image is above and to the left of the Preimage, what can you say about the TranslationVector? When the Image is below and to the right of the Preimage, what can you say about the TranslationVector? When the Image is below and to the left of the Preimage, what can you say about the TranslationVector? Drag the TranslationVector back to (3,1) Write the coordinates of A(1,2) and A'( Write the coordinates of B(1,4) and B'( Write the coordinates of C(2,5) and C'( Write the coordinates of D(3,4) and D'( Write the coordinates of E(2,3) and E'( Write the coordinates of F(2,2) and F'( How can you combine the coordinates of A with the TranslationVector(3,1) to get the coordinates of A'? How can you combine the coordinates of B with the TranslationVector(3,1) to get the coordinates of B'? How can you combine the coordinates of any Preimage point with the TranslationVector(3,1) to get the coordinates of the Image point? If there were a Preimage point P(x,y) and a TranslationVector(3,1), what would be the coordinates of P'? If there were a Preimage point P(x,y) and a TranslationVector(h,k), what would be the coordinates of P'? Drag the TranslationVector until the Image is exactly on top of the Preimage. What is the TranslationVector? This translation is called the IDENTITY Translation. How is this like the Identity Property of Addition? (You may need to check your textbook Page 19 to remember what this is.) Move the Image so that it is 2 to the right and 3 up. INVERSE translations undo each other. An Inverse vector will go from the Image back to the Preimage. In the left panel, scroll down until you find InverseTranslationVector. Click the hollow circle to the left of the name so that the vector becomes visible. When the TranslationVector is (2,3)? What is the InverseTranslationVector? Move the TranslationVector to (-2,3)? What is the InverseTranslationVector? Move the TranslationVector to (-2,-3)? What is the InverseTranslationVector? Move the TranslationVector to (2,-3)? What is the InverseTranslationVector? When the TranslationVector is (x,y), what is the InverseTranslationVector?