Transformations Review. Points that are rotationally symmetrical will be diagonal from each other
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1 1) This figure represents the floor plan of a museum. Rectangles ABGH and LDEK have diagonals that intersect at point N. The designer wants the stairwells to be rotationally symmetric about N. Which pair of points would be appropriate places for the stairwells? Points that are rotationally symmetrical will be diagonal from each other 2) This figure represents the floor plan of a museum. Rectangles ABGH and LDEK have diagonals that intersect at point N. The designer wants to place sculptures in the corners that are rotationally symmetric about N. Which pair of points would be appropriate places for the sculptures? 3) This figure represents the floor plan of a museum. Rectangles ABGH and LDEK have diagonals that intersect at point N. The designer wants the stairwells to be rotationally symmetric about N. Which pair of points would be appropriate places for the stairwells? 4) AE is a line of symmetry in this diagram. If DF=10, CD=6, CB=4, and AH =3, what is the perimeter of the polygon? A line of symmetry will divide a shape into equal parts so fill in missing side lengths with existing side lengths
2 5) AE is a line of symmetry in this diagram. If DF=8, CD=7, CB=5, and AH =4, what is the perimeter of the polygon? 6) AE is a line of symmetry in this diagram. If DF=14, CD=8, CB=3, and AH =2, what is the perimeter of the polygon? 7) How many lines of symmetry does the polygon have? Equilateral Triangle 8) How many lines of symmetry does the polygon have? Isosceles Trapezoid 9) How many lines of symmetry does the polygon have? Rectangle
3 10) How many lines of symmetry does the polygon have? Parallelogram 11) An isometry is a transformation of an object in which the original object and its image are congruent. Identify the transformations that are or are not isometries. Translation Reflection Rotation Dilation 12) Hexagon ABCDEF is reflected across the x-axis to create A I B I C I D I E I F I, which is then rotated 90 degrees counterclockwise about point F. Graph the final image. After reflection shape is upside down, then turn it on its side towards quadrant IV for a clockwise rotation. 13) Hexagon ABCDEF is reflected across the y-axis to create A I B I C I D I E I F I, which is then rotated 90 degrees counterclockwise about point F. Graph the final image.
4 14) Hexagon ABCDEF is reflected across the x-axis to create A I B I C I D I E I F I, which is then rotated 90 degrees clockwise about point F. Graph the final image. 15) Which letter has rotational symmetry but NOT reflectional symmetry? A O Z C 16) Which letter has rotational symmetry but NOT reflectional symmetry? N H P T 17) Which letter has rotational symmetry but NOT reflectional symmetry? S E D K
5 18) Pre-image point (x,y) is reflected across the line y=-x. Then the new point is translated s units right and t units down. What are the coordinates of the final image? 19) Pre-image point (x,y) is reflected across the line y=-x. Then the new point is translated s units right and t units up. What are the coordinates of the final image? 20) Pre-image point (x,y) is reflected across the line y=-x. Then the new point is translated s units left and t units down. What are the coordinates of the final image? 21) A line segment has endpoints with coordinates (1,4) and (5,8). If the segment is reflected over the y-axis and then reflected over the x-axis, what are the coordinates of the endpoints of the resulting line segment? 22) A line segment has endpoints with coordinates (2,4) and (5,7). If the segment is reflected over the y-axis and then reflected over the x-axis, what are the coordinates of the endpoints of the resulting line segment? 23) A line segment has endpoints with coordinates (1,3) and (4,8). If the segment is reflected over the y-axis and then reflected over the x-axis, what are the coordinates of the endpoints of the resulting line segment? 24) The coordinates of point A are (-2,a). Point B is created by reflecting point A across the x-axis and then translating the image 2 units to the right. What are the coordinates of point B?
6 25) The coordinates of point A are (-3,a). Point B is created by reflecting point A across the x-axis and then translating the image 3 units to the right. What are the coordinates of point B? 26) The coordinates of point A are (-4,a). Point B is created by reflecting point A across the x-axis and then translating the image 2 units to the left. What are the coordinates of point B? 27) The pre-image point P(x,y) is dilated by a factor of 3 and then translated up 6 units. Which transformation also produces image point P(x,y)? (Note: All dilations are centered at the origin.) 28) The pre-image point P(x,y) is dilated by a factor of 4 and then translated up 12 units. Which transformation also produces image point P(x,y)? (Note: All dilations are centered at the origin.) 29) The pre-image point P(x,y) is dilated by a factor of 3 and then translated up 9 units. Which transformation also produces image point P(x,y)? (Note: All dilations are centered at the origin.) 30) The ratio of perimeters of two similar farm fields is 3:5. What is the ratio of their areas? 31) The ratio of perimeters of two similar farm fields is 4:7. What is the ratio of their areas? 32) The ratio of perimeters of two similar farm fields is 4:5. What is the ratio of their areas?
7 33) The local newspaper sells ads at a constant rate per square inch. A 3-inch x 4-inch ad costs $25. Susan has a budget of $150 to run a 9-inch x 12-inch ad. Can she purchase a 9-inch x 12-inch ad and stay within her budget? Use area to determine the cost of the ad, simplify ratio of sides first then find ratio of area by squaring. If $25 connects to the 1 the new price would be 9 times bigger to match the ratio of 1:9 34) The local newspaper sells ads at a constant rate per square inch. A 3-inch x 4-inch ad costs $25. Susan has a budget of $150 to run a 6-inch x 8-inch ad. Can she purchase a 6-inch x 8-inch ad and stay within her budget? 35) The local newspaper sells ads at a constant rate per square inch. A 2-inch x 4-inch ad costs $25. Susan has a budget of $150 to run a 6-inch x 12-inch ad. Can she purchase a 6-inch x 12-inch ad and stay within her budget?
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