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Course Graphing Translation 6 th Grade Math HOMEWORK Page 629 #14-16

Course Tables and Functions Our Learning Goal Students will understand functions by creating tables and graphing translations.

Course Tables and Functions Students will understand functions by creating tables and graphing translations. Learn to use data in a table to write an equation for a function and to use the equation to find a missing value. Learn to represent linear functions using ordered pairs and graphs. Learn to use translations to change the positions of figures on a coordinate plane. Learn to use reflections to change the positions of figures on a coordinate plane. Learn to use rotations to change positions of figures on a coordinate plane. Learn to visualize and show the results of stretching or shrinking a figure.

Today’s Learning Goal Assignment Learn to use translations to change the positions of figures on a coordinate plane. Course Graphing Translation

12-3 Graphing Translations Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up 1. Use the given x-values to write solutions of the following equation as ordered pairs. y = 6x – 2 for x = 0, 1, 2, 3 2. Determine whether (3, –13) is a solution to the equation y = –4x – 1. (0, –2), (1, 4), (2, 10), (3, 16) yes Course Graphing Translation

Problem of the Day Samantha’s house is 3 blocks east and 5 blocks south of Tyra. If Tyra walks straight south and then straight east to Samantha’s house, does she walk more blocks east or more blocks south? How many more? south; 2 blocks Course Graphing Translation

A translation is a movement of a figure along a straight line. You can translate a figure on a coordinate plane by sliding it horizontally, vertically, or diagonally. Course Graphing Translation

Additional Example 1: Translating Figures on a Coordinate Plane Give the coordinates of the vertices of the figure after the given translation. Translate triangle DEF 4 units left and 3 units up F D E y x Course Graphing Translation

Additional Example 1 Continued To move the triangle 4 units left, subtract 4 from each of the x-coordinates. To move the triangle 3 units up, add 3 to each of the y-coordinates. DEFD’E’F’D’E’F’ D(1, 4) E(4, 2) F(–3, –3) D’(1 – 4, 4 + 3)D’(–3, 7) E’(0, 5) F’(–7, 0) E’(4 – 4, 2 + 3) F’(-3 – 4, –3 + 3) Course Graphing Translation

Additional Example 1 Continued E’E’ F’F’ D’D’ y x F D E Course Graphing Translation

Try This: Example 1 Give the coordinates of the vertices of the figure after the given translation. Translate triangle GHJ 3 units left and 3 units up J G H y x Course Graphing Translation

Try This: Example 1 To move the triangle 3 units left, subtract 3 from each of the x-coordinates. To move the triangle 3 units up, add 3 to each of the y-coordinates. GHJG’H’J’ G(2, 4) H(4, 4) J(–3, –2) G’(2 – 3, 4 + 3)G’(–1, 7) H’(1, 7) J’(–6, 1) H’(4 – 3, 4 + 3) J’(–3 – 3, –2 + 3) Course Graphing Translation

Try This: Example 1 Continued H’H’ J’J’ G’G’ y x J G H x Course Graphing Translation

Additional Example 2: Music Application Members of a marching band begin in a trapezoid formation represented by trapezoid KLMN. Then they move 4 steps right and 5 steps down. Give the coordinates of the vertices of the trapezoid after such a translation M K L y x N Course Graphing Translation

Additional Example 2 Continued To move 4 steps right, add 4 to each of the x-coordinates. To move 5 steps down, subtract 5 from each of the y-coordinates. KLMNK’L’M’N’ K(–2, 1) L(1, 1) M(3, –3) K’(–2 + 4, 1 – 5)K’(2, –4) L’(5, –4) M’(7, –8) L’(1 + 4, 1 – 5) M’(3 + 4, –3 – 5) N(–4, –3)N’(0, –8)M’(–4 + 4, –3 – 5) Course Graphing Translation

Additional Example 2 Continued M K L y x N -7 M’M’ K’K’L’L’ N’N’ -8 x Course Graphing Translation

Try This: Example 2 Members of a flag team begin in a trapezoid formation represented by trapezoid KLMN. Then they move 3 steps right and 2 steps down. Give the coordinates of the vertices of the trapezoid after such a translation M K L y x N Course Graphing Translation

Try This: Example 2 To move 3 steps right, add 3 to each of the x-coordinates. To move 2 steps down, subtract 2 from each of the y-coordinates. KLMNK’L’M’N’ K(–1, 3) L(1, 3) M(3, –1) K’(–1 + 3, 3 – 2)K’(2, 1) L’(4, 1) M’(6, –3) L’(1 + 3, 3 – 2) M’(3 + 3, –1 – 2) N(–3, –1)N’(0, –3)M’(-3 + 3, –1 – 2) Course Graphing Translation

Try This: Example 2 Continued M K L y N x M’ K’K’ L’L’ N’N’ Course Graphing Translation

Lesson Quiz Give the coordinates of the vertices of triangle ABC, with vertices A(-5, -4), B(-3, 2), and C(1, -3), after the given translations. 1. Translate triangle ABC 3 units up and 2 units right. 2. Translate triangle ABC 5 units down and 3 units left. 3. Translate triangle ABC 2 units down and 4 units right. A’(-3, -1), B’(-1, 5), and C’(3,0) Insert Lesson Title Here A’(-8, -9), B’(-6, -3), and C’(-2,-8) A’(-1, -6), B’(1, 0), and C’(5,-5) Course Graphing Translation