12-2 Translations A translation is a slide that takes place along a vector. The mapping rules are written as any ONE of the following: Translation Rule: Arrow Notation: Component Form: Holt Geometry Ta,b (x,y)(x+a, y+b) a, b 12-2 Translations
The symbol for a vector is Holt Geometry 12-2 Translations The horizontal movement from J to K is a positive 3 (to the right). 4 3 The vertical movement from J to K is a positive 4 (upwards). Therefore, the component form of this translation is: JK
Holt Geometry 3, 4 12-2 Translations Holt Geometry 12-2 Translations Postulate: A translation is a Rigid Motion Image Preimage
(Isometry) Holt Geometry 12-2 Translations Rigid Motion (Isometry) A rigid motion preserves length and angle measure. A rigid motion maps lines to lines, rays to rays and segments to segments. The image has the same size and shape as the preimage. Holt Geometry 12-2 Translations
Example 1: Identifying Translations Tell whether each transformation appears to be a translation. Explain. A. No; the figure appears to be a reflection. Holt Geometry B. Yes; the figure appears to slide. 12-2 Translations
Example 2: Identifying Translations Tell whether each transformation appears to be a translation. a. Yes; all of the points have moved the same distance in the same direction. Holt Geometry b. No; not all of the points have moved the same distance.
12-2 Translations Example 3 Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,1), and U(3, 1) using the vector -3,-3. R The image of (x, y) is (x 3, y 3). R(2, 5) R(1, 2) S(0, 2) S(3, 1)
T(1, 1) U(3, 1) Holt Geometry R S U S U T(2, 4) U(0, 2) T T 12-2 Translations
, in all 3 ways. A ( 4, 3) A ( 0, 4) B ( 7, 1) B ( 3, 2) C ( 4, 1) C ( 0, 2) The rule mapping ABC onto ABC is: (x, y) ( x 4, y + 1) or
T -4, 1 or -4, 1 Holt Geometry 12-2 Translations Example 4 A transformation maps P(x,y) onto P(x-4,y+2). Under the same transformation, what are the
coordinates of Q, the image of Q(2, -3)? Q(2-4,-3+2) = Q(-2,-1) Holt Geometry 12-2 Translations Example 5 If the coordinates of the vertices of DEF are D(3, 1), E(5, 3), and F(2, 2), what is the image of DEF under the transformation T3,-1? The image of (x, y) is (x + 3, y 1). D(3, 1) E(5, 3)
F(2, 2) Holt Geometry D(0, 2) E(8, 4) F (1, 3)