9-2 Translations You found the magnitude and direction of vectors. Draw translations. Draw translations in the coordinate plane.

Definition A translation is a transformation that moves all the points in a plane a fixed distance in a given direction (slide). The arrow shows the direction of the translation.

Definition A B Initial point or tail Terminal point or tip A vector can be represented as a “directed” line segment, useful in describing paths. A vector has both direction and magnitude (length).

Direction and Length From the school entrance, I went three blocks north. The distance (magnitude) is: Three blocks The direction is: North

Direction and Magnitude The magnitude of AB is the distance between A and B. The direction of a vector is measured counterclockwise from the horizonal (positive x-axis).

B A 45° 60° N S E W A B

Drawing Vectors Draw vector YZ with direction of 45° and length of 10 cm. 1.Draw a horizontal dotted line 2.Use a protractor to draw 45° 3.Use a ruler to draw 10 cm 4.Label the points 45° Y Z 10 cm

Translation vector Since vectors have a distance and a direction, they are often used to describe translations. The vector shows the direction of the translation and its length gives the distance each point travels. To measure direction, add a horizontal dotted line and measure counterclockwise

p. 632

Draw a Translation Copy the figure and given translation vector. Then draw the translation of the figure along the translation vector. Step 2Measure the length of vector. Locate point G' by marking off this distance along the line through vertex G, starting at G and in the same direction as the vector. Step 1Draw a line through each vertex parallel to vector. Step 3Repeat Step 2 to locate points H', I', and J' to form the translated image. Answer:

Which of the following shows the translation of ΔABC along the translation vector? A.B. C.D.

p. 633

Translations in the Coordinate Plane A. Graph ΔTUV with vertices T(–1, –4), U(6, 2), and V(5, –5) along the vector  –3, 2 . The vector indicates a translation 3 units left and 2 units up. (x, y)→(x – 3, y + 2) T(–1, –4)→(–4, –2) U(6, 2)→(3, 4) V(5, –5)→(2, –3) Answer:

B. Graph pentagon PENTA with vertices P(1, 0), E(2, 2), N(4, 1), T(4, –1), and A(2, –2) along the vector  –5, –1 . The vector indicates a translation 5 units left and 1 unit down. (x, y)→(x – 5, y – 1) P(1, 0)→(–4, –1) E(2, 2)→(–3, 1) N(4, 1)→(–1, 0) T(4, –1)→(–1, –2) A(2, –2)→(–3, –3) Answer:

Describing Translations A. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 2 to position 3 in function notation and in words. The raindrop in position 2 is (1, 2). In position 3, this point moves to (–1, –1). Use the translation function (x, y) → (x + a, y + b) to write and solve equations to find a and b. (1 + a, 2 + b) or (–1, –1) 1 + a = –1 2 + b = –1 a = –2 b = –3 Answer: function notation: (x, y) → (x – 2, y – 3) So, the raindrop is translated 2 units left and 3 units down from position 2 to 3.

B. ANIMATION The graph shows repeated translations that result in the animation of the raindrop. Describe the translation of the raindrop from position 3 to position 4 using a translation vector. (–1 + a, –1 + b) or (–1, –4) –1 + a=–1–1 + b=–4 a=0b=–3 Answer: translation vector:

B. The graph shows repeated translations that result in the animation of the soccer ball. Describe the translation of the soccer ball from position 3 to position 4 using a translation vector. A.  –2, –2  B.  –2, 2  C.  2, –2  D.  2, 2 

9-2 Assignment Page 627, even, 20, 21, 26, 27