Linear Algebra Problem 3.4

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Linear Algebra Problem 3.4 Monday, September 8

Problem 3.3 answers

Problem 3.3 ACE answers #6, #7

Learning Target I will recognize that lines and their images under translations and half turns are related to one another.

3.4 What we have observed about transformations so far…. Read page 56. Our study of flips, turns and slides showed that those transformations do not change the size or shape of a figure – they are congruent. Line segments move to line segments. Angles move to angles Translations and half-turn rotations have a special effect on lines.

Problem 3.4 Special Properties of half-turns and translations What is the special relationship among the corresponding sides of the three figures? How can you use the coordinates of the vertices to prove your conjecture?

Problem 3.4 A Look at line segment AB and its image after a translation, line segment FG. In investigation 1, you observed that a segment and its image after a translation appear to be congruent and parallel. Use the coordinates of the endpoints and slopes of lines to prove this observation is correct. A B C D E Coordinate pair (-1,5) (1,1) (5,2) (4,6) (1,7) F G H I J (-8,4) (-6,0) (-2,1) (-3,5) (-6,6)

Answer for 3.4 A

Problem 3.4 B

Answer for Problem 3.4 B

Problem 3.4 C and Answer

Problem 3.4 D and answer

Rate Your Learning I will recognize that lines and their images under translations and half turns are related to one another.

Homework for Problem 3.4 ACE p. 61 #10