10-8 Translations. (pages 451-454). Indicator G8- Perform translations of two- dimensional figures using a variety of methods. Any time a geometric figure is moved, it is called a transformation .
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10-8 Translations (pages 451-454) Indicator G8- Perform translations of two- dimensional figures using a variety of methods
Any time a geometric figure is moved, it is called a transformation. When you slide a polygon to a new position without turning it, the sliding motion is called a translation. When translating a figure, every point of the original figure is moved the samedistance and in the same direction! Whenever a figure is translated, use the prime symbols for the vertices in the transformed image. Translation (slide) Transformation/Translation Notation
Graph a Translation • Translate 5 units left and 1 unit up. • Move each vertex of the figure 5 units left and 1 unit up. • Label the new vertices A’, B’, and C’. • Connect the vertices to draw the triangle. The coordinates of the vertices of the new figure are • A’ (-4, -1), B’ (-1, 2), and • C’ (0, -1). B’ B A’ C’ A C Note that after the triangle has been translated, the original triangle and the translated triangle (image) are congruent.
You can also find the coordinates of a translation by adding or subtracting. Tip- A positiveinteger describes a translation right or up on a coordinate plane. A negativeinteger describes a translation left or down. H I G’ (1, -2) (-4 + 5) (1 – 3) H’ G J I’ H’ (1, 0) (-4 + 5) (3 – 3) (-2 + 5) (3 – 3) I’ (3, 0) G’ J’ (-1 + 5) (1 – 3) J’ (4, -2)
You try… The squares below represent the desks in a classroom. Ana is seated at the square marked X. She is moved to the seat marked Y. Describe this translation as an ordered pair. Remember (X,Y). Ana moved 2 places right. (this is +2) And 2 places up. (this is +2) So, the translation can be written (2,2).