Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane Remember, in Math the word dilate means to __________________________________ or ________________________________________ a figure. When you expand or shrink something, the __________________________________ tells you by how much you need to expand or shrink it. When scale factors are ____________________________ than 1, your figure gets bigger. Examples: _________________________________________________________________ When scale factors are ____________________________ than 1, your figure gets smaller. Examples: _________________________________________________________________ Example 1: Dilate a figure with a scale factor > 1 (Expand) y-axis Step 1: Identify and record each point’s coordinates J K -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 1 2 3 4 5 6 7 8 9 x-axis L -3 How Do I Dilate? Step 2: Identify the scale factor and predict if it will expand or shrink. -4 -5 -6 -7 -8 -9 Graph the dilated image of triangle JKL using a scale factor of 2 and (0,0) as the center of dilation. J: __________ J’: __________ K: __________ K’: __________ L: __________ L’: __________ Step 3: Multiply the coordinates by the scale factor and record the new coordinates. Step 4: Plot the new points, connect the dots, and label the image in prime notation. Step 5: Check your work. Does your image match your prediction? Does it make sense? 1 Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane You Try 1! y-axis y-axis M X N P -9 -8 -7 -6 -5 -4 -3 -2 Y -1 0 -1 1 2 -2 3 4 5 6 7 8 9 x-axis -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 x-axis -2 O -3 -1 0 -1 -3 -4 -4 -5 Z -5 -6 -6 -7 -7 -8 -8 -9 -9 Graph the dilated image of quadrilateral MNOP using a scale factor of 3 and the origin as the center of dilation. Graph the dilated image of triangle XYZ using a scale factor of 1.5 and (0,0) as the center of dilation. M: __________ M’: __________ X: __________ X’: __________ N: __________ N’: __________ Y: __________ Y’: __________ O: __________ O’: __________ Z: __________ Z’: __________ P: __________ P’: __________ Example 2: Dilate a figure with a scale factor < 1 (Shrink) y-axis Graph the dilated image of triangle JKL using a scale factor of 0.5 and (0,0) as the center of dilation. J L -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 1 2 3 4 5 6 7 8 9 J: __________ J’: __________ K: __________ K’: __________ L: __________ L’: __________ x-axis -3 K -4 -5 -6 -7 -8 -9 2 Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane You Try 2! y-axis y-axis M X P -9 -8 -7 -6 -5 -4 N -3 -2 -1 0 -1 1 2 3 4 5 6 7 Y 8 9 -9 -8 -7 -6 -5 -4 x-axis -3 -2 -1 0 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 1 2 3 4 5 6 7 8 9 -7 O Z -8 -8 -9 -9 Graph the dilated image of quadrilateral MNOP using a scale factor of 1/3 and the origin as the center of dilation. Graph the dilated image of triangle XYZ using a scale factor of .5 and (0,0) as the center of dilation. M: __________ M’: __________ X: __________ X’: __________ N: __________ N’: __________ Y: __________ Y’: __________ O: __________ O’: __________ Z: __________ Z’: __________ P: __________ P’: __________ Example 3: Identify and describe a dilation. y-axis Given the coordinates for each set of vertices, choose the appropriate transformation. J’ L’ Triangle QRS J L -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 8 9 x-axis Triangle Q’R’S’ Q: (6, 4) Q’: (3, 2) R: (0, 2) R’: (0, 1) S: (-8, -4) S’: (-4, -2) -2 K K’ -3 -4 -5 -6 -7 -8 -9 A B C D Dilation with a scale factor of 2 Dilation with a scale factor of 0.5 Translation 1 unit down Translation 3 units left Describe the dilation of triangle JKL, using the origin as the center. ________________________________________ 3 x-axis Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane You Try 3! y-axis P Given the coordinates for each set of vertices, choose the appropriate transformation. M P’ Triangle DEF M’ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 O’ 1 2 3 4 5 6 7 8 9 x-axis N’ Triangle D’E’F’ D: (6, 2) D’: (3, 1) E: (-1, 4) E’: (-4, 3) F: (-6, -3) F’: (-9, -4) -3 -4 N -5 -6 -7 -8 O -9 Describe the dilation of quadrilateral MNOP, using the origin as the center. A B C D Dilation with a scale factor of 0.5 Dilation with a scale factor of 2 Translation 3 units to the left, 1 unit down Translation 3 units to the right, 1 unit down ________________________________________ Sample Test Question: 4 Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane Independent Practice y-axis 1) y-axis 2) J’ A’ B’ A B J L’ L -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 x-axis -3 -2 -2 K C -4 -5 2 3 4 5 6 7 8 9 -3 -4 -6 C’ -7 -7 -8 -8 -9 K’ -9 Describe the dilation of quadrilateral ABCD, using the origin as the center. Describe the dilation of triangle JKL, using the origin as the center. ________________________________________ ________________________________________ y-axis 3) x-axis -5 -6 D’ 1 -2 -3 D -1 0 -1 y-axis 4) N’ X’ X N M’ -9 -8 -7 -6 -5 -4 M -3 -2 P O’ O -1 0 -1 1 2 3 4 5 7 8 9 x-axis -9 -8 -7 -6 -5 -4 -2 Z -5 -6 -7 -3 -2 -1 0 -1 3 4 5 6 7 8 9 x-axis -4 -5 Z’ -6 -7 -8 -9 -9 ________________________________________ 2 -3 -8 Describe the dilation of quadrilateral MNOP, using the origin as the center. 1 -2 -3 -4 P’ Y’ Y 6 Describe the dilation of triangle XYZ, using the origin as the center. ________________________________________ 5 Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane y-axis 5) y-axis 6) D D’ A A’ B B’ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 8 9 x-axis F’ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -2 -3 -3 C’ -4 -6 -7 -7 C F 4 5 6 7 8 9 x-axis -8 E -9 3 -5 -6 -8 2 -4 E’ -5 1 -9 Describe the dilation of triangle ABC, using the origin as the center. Describe the dilation of triangle DEF, using the origin as the center. ________________________________________ ________________________________________ 7) Given the coordinates for each set of vertices, choose the appropriate transformation. Triangle QRS Triangle Q’R’S’ Q: (-2, 4) Q’: (-4, 8) R: (4, 0) R’: (2, 4) S: (6, 2) S’: (4, 6) y-axis 9) A Dilation with a scale factor of 2 B Dilation with a scale factor of 0.5 C Translation 2 units left, 4 units up D Translation 2 units right, 4 units up -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 8 9 x-axis -2 -3 -4 -5 8) Given the coordinates for each set of vertices, choose the appropriate transformation. -6 -7 -8 Triangle ABC Triangle A’B’C’ A: (9, 3) A’: (3, 1) B: (0, -6) B’: (0, -2) C: (-3, 0) C’: (-1, 0) A Dilation with a scale factor of 3 B Dilation with a scale factor of 1/3 -9 Create your own shape. Choose a scale factor and dilate. Then, describe your dilation on the lines below. ________________________________________ ________________________________________ C Translation 2 units right D Translation 4 units up 6 Name: __________________________________________ Unit 6: Transformational Geometry Date: ___________________________ Lesson #4: SWBAT perform dilations on the coordinate plane Homework: Homework #6.4 Exit Ticket 7
