12.1.2 Translations (continued) Example 3 Drawing Translations in the Coordinate Plane
A figure in the coordinate plane is translated in this example. The coordinates of the vertices of the preimage and the translation vector are given. The translation vector, 〈 1, − 5 〉 , can be used to derive a rule for the translation of the coordinates: ( x , y ) → ( x + 1, y − 5). Apply the rule to translate each of the three preimage vertices to the image vertices. For example, A ( − 4, 1) → A ′( − 4 + 1, 1 − 5) = A ′( − 3, − 4). Draw line segments between the image vertices to form the translated figure.
Example 4 Entertainment Application
The translation vector for the sum of a sequence of position changes in the coordinate plane is determined in this application example. The starting point coordinates and the changes in x or y of each movement are given. Draw the given information in the coordinate plane to better visualize it. The starting point coordinates are given as (7, − 7). The drummer’s movements take her to the end point with coordinates ( − 7, 14). To find the vector that gives the translation (7, − 7) → ( − 7, 14), subtract the x and y coordinates of the starting point from the x and y coordinates of the end point. The vector is: 〈− 7 − 7, 14 − ( − 7) 〉 = 〈− 14, 21 〉 .
294
Made with FlippingBook - PDF hosting