Exercise 9 Page 548

We are given the a point and its image after a translation. P( -3, 6) → P'( 0, 1) We want to find the component form of the vector that translates P to P'. To do so, we must examine what changes between the x-coordinates and the y-coordinates when going from P to P'. Let's write the coordinates of the image as a sum between the preimage coordinates and one missing number. x: & -3 + = 0 y: & 6 + = 1 For the x-coordinate, we started at -3 and ended at 0. This means that the translation added 3 units. x: & -3 + 3 = 0 y: & 6 + = 1 For the y-coordinate, we started at 6 and ended at 1. This means that we moved 5 units down. Therefore, we should subtract 5. x: & -3 + 3 = 0 y: & 6 + ( -5) = 1 The component form of a vertex is written as ⟨ , ⟩ with the translation values for x and y in the blanks. The component form for the translation from P to P' is ⟨3,-5⟩.