Day 1 Translations, Reflections, and Rotations
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1 Name Date Day 1 Translations, Reflections, and Rotations There are many different ways to move a figure on the coordinate plane. Some movements keep the figure the same size and some may make the figure bigger or smaller. These movements are called transformations. Transformations are the mapping or movement of all the points in a figure on the coordinate plane. When a figure is the original figure, it is called the pre-image. The prefix pre means. In the above picture, we would label the points as,, and. When a figure has been transformed, it is called the image. We would label the new points as,, and. We would say that points,, and have been mapped to the new points,, and Exploring Translations. Graph triangle by plotting points (8, 10), (1, 2), and (8, 2).. Translate triangle 10 units to the left to form triangle and write new coordinates.. Translate triangle 12 units down to form triangle and write new coordinates. oordinates of Triangle (8, 10) oordinates of Triangle oordinates of Triangle (1, 2) (8, 2)) Observation: Did the figures change size or shape after each transformation?
2 You observed that your four triangles maintained the same shape and size. When a figure keeps the same size and shape, it is called a rigid transformation. With your experiment, you were performing a translation. translation is a slide that maps all points of a figure the same distance in the same direction. translation can slide a figure horizontally, vertically, or both. Rule for Translations: (x, y) (x + a, y + b) a left or right translations (horizontally) b up or down translations (vertically) Practice with Translations Name the rule for the given figures: Practice 1. Translate the image by (x 8, y + 2) 2,4 ' 0, 8 ' 3,5 ' 2. Translate the image by (2x + 2, y 3) D 1,2 D' E 3, 5 E' F 4, 1 F' 3. Find the pre-image (x + 12, y 17) G G'(5, 29) H H'(20, 19) I I' (21, -4)
3 Reflections and Rotations Figures that are mirror images of each other are called reflections. reflection is a transformation that flips a figure over a reflection line. reflection line is a line that acts as a mirror so that corresponding points are the same distance from the mirror. Reflections maintain shape and size; they are our second type of rigid transformation. Reflection over y-axis Reflect parallelogram D over the y-axis using reflection lines. Record the points in the table. D Reflection over x-axis Reflect parallelogram D over the x-axis using reflection lines. Record the points in the table D
4 Reflection over y = x Reflect the triangle over the y = x using reflection lines. Record the points in the table Reflection over y = -x Reflect triangle over the y = -x using reflection lines. Record the points in the table Reflection over Horizontal and Vertical Lines Reflect over x = -1 Reflect over y = 2
5 Practice with Reflections Given triangle MNP with vertices of M(1, 2), N(1, 4), and P(3, 3), reflect across the following lines of reflection: x-axis y-axis y = x y = -x (x, y) (x, y) (x, y) (x, y) M(1, 2) M(1, 2) M(1, 2) M(1, 2) N(1, 4) N(1, 4) N(1, 4) N(1, 4) P(3, 3) P(3, 3) P(3, 3) P(3, 3) Rotations rotation is a circular movement around a central point that stays fixed and everything else moves around that point in a circle. rotation maintains size and shape; therefore, it is our third type of rigid transformation. When we rotate our figures around a fixed point, we classify our rotation by direction and degree of rotation. Degrees of Rotation Direction of Rotation It is important to understand that some rotations are the same depending on the degree and direction of the rotation. Most of the time, rotations are given using counterclockwise direction. Here are equivalent rotations: 90ounterclockwise = 270 lockwise 90 lockwise = 270 ounterclockwise 180ounterclockwise = 180 lockwise Rules for Rotations 90W / 270W 180W / 180W 90W/270W (x, y) (-y, x) (x, y) (-x, -y) (x, y) (y, -x)
6 Practice with Rotations a. Rotate 90 W b. Rotate 180 W c. Rotate 90W Lines of Symmetry line of symmetry is a line you can use to fold a figure so that both halves match up perfectly. This means the figure is symmetrical (balanced/matching) on both sides of the line. Example: How many lines of symmetry does each shape have?
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