transformations

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Transformations:

Transformations Austin Uresti

Part 1: Reflections:

Part 1: Reflections A Reflection (a.k.a. “flip”) is a transformation in which a mirror image is produced by flipping a figure over a line (The Line Of Reflection) How to Reflect: 1)Count the number of units between each vertex and the line of reflection.(If reflecting across the x-axis, the x coordinate stays the same and the y-coordinate changes; and vice versa for reflecting across the y-axis.) 2)Plot a point for each vertex the same distance away from the Line of Reflection on the other side 3)Connect the new points to form the reflected figure

Part 1:Reflections (Visual):

Part 1:Reflections (Visual) THIS IS THE LINE OF REFLECTION A B C D A is 4 units away from the line of Reflection B is 5 units away from the line of Reflection C is 3 units away from the line of Reflection D is 4 units away from the line of Reflection A’ B’ C’ D’ The Reflected image looks exactly like the original except flipped. *Notice that the new figure is on the same y-coordinate because it is reflected across the y-axis A’ is 7 units away from the line of Reflection B’ is 7 units away from the line of Reflection C’ is 5 units away from the line of Reflection D’ is 4 units away from the line of Reflection A’’ B’’ C’’ D’’ The Reflected image looks exactly like the original except flipped. *Notice that the new figure is on the same x-coordinate because it is reflected across the x-axis

Part 2:Dilations:

Part 2:Dilations A dilation is the act of enlarging or reducing a figure How To Dilate: *You will use a scale factor when dilating(We will use 3/2) 1)Find the ordered pair of each vertex (i.e. 2,4) 2)Convert ordered pair into a fraction 3)Multiply each coordinate by the scale factor (3/2) 2 x 3 = 6 or 3 or 3  x coord . 1 2 2 1

Part 2:Dilations:

Part 2:Dilations 4 x 3 = 12 or 6 or 6  y coord . 1 2 2 1 3)The new ordered pair is: (3,6) 4)Do the same for other vertices 5)Graph the vertices

Part 3:Translations:

Part 3:Translations A translation is when you move every point of a figure the same distance and direction How to translate (two ways) 1)Move each vertex of the original figure in the direction and distance you are told 1)If moving to the left add (-a) [a represents the number you are told] to your (x) coordinate 2)If moving Right add (a) to your (x) coordinate

Part 3:Translations:

Part 3:Translations 3)If moving up add (b) to your (y) coordinate [b represents the number you are told] 4)If moving down add (-b) to your (y) coordinate Translate Triangle ABC 3 left and 4 up

Part 4:Rotations:

Part 4:Rotations Rotating a figure is “spinning” a figure around a point. There are 4 main rotary angles: 90°, 180°, 270°, 360° Each of these have simple rules for rotating 90° Make y coordinate negative, then flip x and y ( X,y ) To (- y ,x ) 180° Make both coordinates negative ( X,y ) To (-x,-y) 270° Make x coordinate negative, then flip x and y ( X,y ) To (y,-x) 360° Do nothing ( X,y ) To ( x,y )

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