1. T RANSLATIONS AND V ECTORS Unit IB Day 7

2. D O NOW : List the six ways to prove a quadrilateral is a parallelogram.

3. T RANSLATIONS A translation is a _________________ that maps every segment PQ to segment P'Q' such that PP' = QQ' PP' || QQ' (or PP' and QQ' are collinear).

4. T RANSLATION T HEOREM A translation is ____________.

5. E X. 1: P ROOF OF THE T RANSLATION T HEOREM (C ASE 1) G IVEN : PQ translated to P'Q' P ROVE : PQ = P'Q'

6. T RANSLATING IN A C OORDINATE P LANE Coordinate notation: ( x, y )  ( x + a, y + b ), where a and b are constants Each point shifts ______ units horizontally and ____ units vertically.

7. E X. 2: T RANSLATIONS IN A C OORDINATE P LANE Sketch a triangle with vertices A (-1, -3), B (1, -1), and C (-1, 0). Then sketch its image after the translation ( x, y )  ( x – 3, y + 4). Δ ABC Δ A'B'C' A (-1, -3) B (1, -1) C (-1, 0)

8. V ECTORS Vector : A quantity that has both ____________ and ____________ (but not position). Represented by an arrow between two points. Notation: ______ initial point terminal point Component form: ______________

9. E X. 3: I DENTIFYING V ECTOR C OMPONENTS Name the vector and write its component form.

10. E X. 4: T RANSLATING U SING V ECTORS Use vector GH = to translate the triangle whose vertices are A (3, -1), B (1, 1), and C (3, 5). What do we notice about the vectors connecting the image to the preimage?

11. E X. 5: F INDING V ECTORS In the diagram, QRST maps onto Q'R'S'T' by translation. Write the component form of the vector that can be used to describe the translation.

12. E X. 6: U SING V ECTORS A boat wants to get from point A to point D. When the boat is 3 miles east and 2 miles north of its starting point ( B ), it gets blown off course to point C. Write the component forms of the two vectors shown. Write the component form of the vector that the boat can follow from C to D.

13. C LOSURE A (-2, 1) and B (3, -1) are translated to A' (1, -2) and B' (6, -4). Describe the translation using coordinate notation. Write the component form of the vector that can be used to describe the translation.