Investigation - Vectors 1. 2. 3. 4. A On an A4 piece of paper, use a ruler to draw any quadrilateral ABCD – with nothing special about it at all, preferably. Carefully mark the exact centre of each edge, and joint up the four points P, Q, R, S. What shape have you now drawn? Repeat for another quadrilateral of your choice. What do you find? B 5. Choose the coordinates of four points A, B, C, D. 6. Draw a sketch of the quadrilateral made. 7. Calculate the coordinates of the midpoints P, Q, R, S, of each line. 8. Calculate the length of each line PQ, QR, RS, SP. 9. Find the gradient of each of these lines PQ, QR, RS and SP. 10.What does all this information tell you about the lines PQ, QR, RS and SP? 11.Repeat for another set of 4 points of your choice. C Q ` C B R P A D S 12.Draw a diagram of a quadrilateral ABCD. Mark AB as vector a, BC as vector b, CD as vector c. 13.Write down the vector AD in terms of a, b, c. 14.If P, Q, R, S are the midpoints as before, find in terms of a, b, c the vectors PQ and SR . 15.What does this tell you about the shape PQRS? Why? 16.How would you explain your conclusions?