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Translations on the Coordinate Plane

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In chess, there are rules governing how many spaces and in what direction each game piece can be moved The diagram below shows the legal moves of the piece known as the knight

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Translations on the Coordinate Plane A translation (sometimes called a slide) is the movement of a figure from one position to another without turning it Every point on the original figure is moved the same distance and in the same direction(s)

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Translations on the Coordinate Plane The new points of the new figure are referred to as “prime” (for example, point A translated below becomes A’ or A prime) The new figure below is referred to as triangle A’B’C’

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Translations on the Coordinate Plane If you think of movements in terms of positive and negative, movements to the right and up are positive, while movements to the left and down are negative In the figure below, triangle ABC has been translated (6, -4)

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Translations on the Coordinate Plane Checkpoint A positive number in the x-coordinate position of an ordered pair (3, 4) means to translate in which direction? A negative number in the x-coordinate position of an ordered pair (-3, 4) means to translate in which direction? RIGHT LEFT

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Translations on the Coordinate Plane Checkpoint A positive number in the y-coordinate position of an ordered pair (3, 4) means to translate in which direction? A negative number in the y-coordinate position of an ordered pair (-3, -4) means to translate in which direction? UP DOWN

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Translations on the Coordinate Plane There are two ways to think of how to translate a figure. Consider the figure below Each vertex of the triangle has been moved 6 units to the right and 4 units down Hence, a translation of (6, -4)

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Translations on the Coordinate Plane Another way to translate a figure in the direction described by an ordered pair is to add the ordered pair to the coordinates of each vertex of the figure In the example below, A(-2, 3) B(-2, 1) and C (-5, 1) make up the original triangle

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Translations on the Coordinate Plane Translate triangle ABC by (6, -4) A(-2, 3)B(-2, 1)C(-5, 1) +(6, -4)+(6, -4)+(6, -4) A’(4,-1)B’(4,-3)C’(1,-3)

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Translations on the Coordinate Plane Checkpoint Describe the translation below using an ordered pair: M A H T M’ A’ H’ T’ (-7, -3)

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Translations on the Coordinate Plane Checkpoint Give the vertices of square MATH after a translation of (2, 2): M A H T M’ (3, 6) A’ (6, 6) T’ (6, 3) H’ (3, 3)

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Translations on the Coordinate Plane Checkpoint Show how to mathematically translate square MATH (2, -7) M A H T M’ (3, -3) A’ (6, -3) T’ (6, -6) H’ (3, -6)

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Homework: Practice Worksheet 11-8 Practice Skills 6-8 Due Tomorrow!!

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