Translations SLIDE. Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3).

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1 Translations SLIDE Every point in the shape must move In the same direction The same distance Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3). Note: the Pre- Image ABC(original figure is solid) and the Image A B C (the translated figure) is dotted. We say ABC is mapped to A B C. Vector notation: A vector is a quantity with magnitude and direction. A vector in component form: < horizontal component, vertical component > The component form of the above vector would be <-5, 3> Complete Questions #1-3 on your stations worksheet

2 Rotations Around a point other than the origin Rotating around a point other than the origin is really nothing more than finding the slope between each coordinate of your figure and the point you are rotating around. Example: Rotate (4, 8) 90 around the point (1,1). Step 1: Find the slope from (1,1) to (4, 8). Step 2: Since we are rotating 90 we want to use the perpendicular slope from (1,1) Step 3: Find the opposite reciprocal slope and count the slope from (1, 1) Step 4: Write down the point where the rotated point will be located. Step 5: Use patty paper to verify your answer. (Hold patty paper at (1,1) and mark point (4, 8). Rotate patty paper 90 ) OR: Draw new axis through (1,1) and rotate from there as before. Plot new point and write your answer is based on original axis. Complete Questions on your stations worksheet

3 Every point in the shape Rotations TURN Is the same distance from the center Most rotations are counterclockwise unless otherwise stated Example: Rotate the figure 90 around the origin (pre-image is dotted figure) **Discuss what happened to each point after the rotation When completing rotations you can memorize rules OR you can simply turn the paper the give number of degrees, write the new points and plot the new points. Complete the stations worksheet.

4 Reflections FLIP Every point in the shape Is the same distance from the line you are reflecting over Has the same size as the original image Example: Reflecting the image over the x and y axis X-Axis If the mirror line is the x-axis, just change each (x,y) into (x,-y) Y-Axis If the mirror line is the y-axis, just change each (x,y) into (-x,y) Example: Reflecting over the line y=x. Use the MIRA to see what happens when you reflect over the line y=x. Discuss what happens to the points of the figure. Complete Questions #4-6 on your stations worksheet

5 Dilations ENLARGEMENT/ REDUCTION A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. Most dilations are around the origin. Dilation using scale factor: Draw a dilation from point O with a scale factor of 2. Directions: Measure distance from O to each point of the pre-image triangle. Then double each measurement and measure out the new distance from point O. Draw a line out and mark where each new point belongs. Connect new points to make image The diagram to the left shows a reduction. The two figures are similar the angles are congruent and the side lengths are proportional. Example: Dilation on the coordinate plane PROBLEM: Draw the dilation image of triangle ABC with the center of dilation at the origin and a scale factor of 2. OBSERVE: Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x 2, y 2). NOTE: The preimage is similar to the image. Complete questions on stations worksheet