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Translating Figures Translation: move (SLIDE) all points of the original figure MCAS Review the same distance in the same direction. Key Concept Translation in the Coordinate Plane Transformations Words to translate a point along vector (a, b), add a to the x-coordinate and b to the P 1 - 2 + 7, 3 + 4) or ( 5 . 7) y-coordinate. Symbols ( xy) - (x+ ay+b) P 1 - 2 , 3 ) Example The image of P(-2. 3) translated along vector (7, 4) is P'(5, 7) Example #1 O Example #2 Ex. 1: Ex. 2: Graph ATUV with vertices Graph pentagon PENTA with T (-1, -4), U (6, 2), and vertices P (1, 0), E (2, 2), N ( 4, 1), V (5, -5) along the vector T(4, -1), and A (2, -2) along the ( - 3 , 2 ) . vector (-5, -1). Example #3 Practice #1 Ex. 3: The preimage of rectangle ABCD has vertices at Graph each figure and its image along the given vector. A (-4, 5), B (-4, -3), C (1, -3), and D (1, 5). a. AEFG with vertices E(-7, -1), F(-4, -4), and G(-3, -1); (2, 5) Its image has vertices at A' (-1, 3), B' (-1, -5), C' (4, -5), and D' (4, 3) Write the ordered pair that describes the transformation of the rectangle.Translating Figures Translation: move (SLIDE) all points of the original figure MCAS Review the same distance in the same direction. Key Concept Translation in the Coordinate Plane Transformations Words To translate a point along vector (a, b). add a to the x-coordinate and b to the P 1 - 2 + 7 , 3 + 4 ) or ( 5 , 7 1 y-coordinate. P 1 - 2 . 3 ) Symbols (x y) - (x+ ay+b) Example The image of P(-2. 3) translated along vector (7, 4) is P'(5, 7). O Example #1 Example #2 O Ex. 1: Ex. 2: Graph ATUV with vertices Graph pentagon PENTA with T (-1, -4), U(6, 2), and vertices P (1, 0), E ( 2, 2 ), N ( 4, 1 ) , V (5, -5) along the vector T (4, -1), and A (2, -2) along the vector (-5 , - 1 ) . (- 3 , 2 ) . O Example #3 Practice #1 Ex. 3: The preimage of rectangle ABCD has vertices at A (-4, 5), B (-4, -3), C (1, -3), Graph each figure and its image along the given vector. and D (1, 5). a. AEFG with vertices E(-7, -1), F(-4, -4), and G(-3, -1); (2, 5) Its image has vertices at A' (-1, 3), B' (-1, -5), C' (4, -5), and D' (4, 3) Write the ordered pair that describes the transformation of the rectangle.Practice #3 O Practice #2 Write each translation vector to map the green image to the blue preimge. b. square JKLM with vertices J(3, 4), K(5, 2), L(7, 4), and M(5, 6); (-3, -4) 24. 23. Reflecting Images Reflect over a Horizontal/Vertical Line Reflection: FLIP the preimage over the line of Key Concept Reflection in the x-or y-axis Reflection in the x-axis Reflection in the y-axis reflection Words To reflect a point in the x-axis. Words To reflect a point in the y axis. multiply its y coordinate by -1. multiply its x coordinate by -1. Symbols (x y) - (x -y) ymbols (x. y - (-xy B(7. 3) A(4. 1) A'1-2. 31 A(2. 31 Example Example A'14. -1 B'0. -3 31-6. BIG. - Example #1 Example #2 Ex. 1: Ex. 2: Graph A ABC with vertices Quadrilateral JKLM has A(-5, 3), B(2,0), and C(1, 2) vertices J(2, 3), K(3, 2), L(2, - 1 ) , and its reflection over the and M(0, 1). Graph JKLM and x-axis. its reflection over y = -2.O Reflect over Parent Graph Example #3 O Ex. 3 Key Concept Reflection in Line y= x 4 BCD has vertices Words To reflect a point in the line Example B(-1.4) y My = x y= x interchange the x- and B(- 3, 3), C(1,4), and D(-2,-4) coordinates. A(-5, 2) Symbols (x. y) - (y, x) Graph A BCD and its reflection over the line y = x . O Example #4 MCAS Question #1 Ex. 4: Trapezoid RSTU is shown on the coordinate grid below. Quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, -1), Trapezoid RSTU will be reflected over the x-axis to create trapezoid R'STU'. and D(2, -3). What will be the coordinates of point R', the image of point R after the reflection? Graph ABCD and its reflection A. (4, 5 ) B. (4, - 5 ) over the line y = x. C. (-4, 5) D. (-4, - 5) O MCAS QUESTION #2 MCAS QUESTION #3 Quadrilateral RSTU is graphed on the coordinate grid below. Consider square EFGH, shown on this coordinate plane. Quadrilateral the y-axis and translated 4 units down. What will be the coordinates of the image of point S after the transformations? A. (- 5, -2) B. (1, -2) 12 3456 C. (-1, 2) D. (- 5, 2 ) Square EFGH will be reflected over the y-axis. Which graph correctly shows the image of square EFGH after the reflection?CsHO, Moles Calculated A