Use graph paper. Label each graph correctly, and put each letter below on a different graph! Graph the quadrilateral A (5,4), B(2,3), C (-1, -2) and D(-5, 6) and the following transformation: 1. a) Translation: (x, y) → (x+5, y) Rotation: 900 b) Translation : Reflection y = -1 d) Rotation: 2700 Dilation: Center of dilation at origin and k = 2 e) Reflection over the line y=x Dilation: Center of dilation at origin, and scale factor of 165%
2) Write the name of the vector, and write its component form.
3) Write the rule for the following translation.
4) a) Describe the composition of translations.
b) Write a final rule that would map triangle ABC straight onto its image triangle A’’B’’C’’.
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5) A’ (3,5), B’(6,2) and C’(-1,4) is the image after the translation using the vector . What were the coordinates of the pre-image before the translation?
6) Determine the number of lines of symmetry (if any) for the following pentagon.
7) Describe the congruence transformation that maps triangle DRI to triangle JVK.
8) PQ has been reflected over 2 parallel lines to create the following image. a) What is the relationship between PQ and P”Q”?
b) What is the relationship between PP’ and line a?
c) What is the relationship between PP” and QQ”?
d) What is the relationship between PP” and the distance between line a and line b?
e) What type of transformation maps PQ directly onto P”Q”? 2
9) F has been reflected over two intersecting lines. What is the final angle of rotation from F to F”?
10) You are rotating a figure 1720 from G to G”. Find the measure of the acute angle formed by intersecting lines so that G can be mapped to G” using two reflections.
11) What is the scale factor of the dilation? Is it a reduction or enlargement?
12) Find A (10, 2) and B(10, -6). a) Rotation of 2700 about the origin. b) Reflection over the line y = x followed by a reflection over the line y = 0 c) Reflection over the y-axis
13) Find the corrdinates of A’B’ given A(4,6) and B (6,9) and: a) Dilation about the origin with scale factor of 4. b) Dilation about the origin with scale factor of -2 c) Dilation about the origin with a scale factor of ½. d) Dilation about the origin with a scale factor of 75%.
14. What is the length of ED given that the two triangles are similar?
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15. What is the scale factor for the dilation?
15. You have a picture that is currently 15” x 45”. You want to reduce it using a scale factor of 1/3. What are the new dimensions of the picture?
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17) A car starts at (2,2) on the coordinate grid, and travels south 5 miles and east 2 miles. Then, it immediately travels 4 more miles east and north 1 mile before stopping at it’s final destination. a) Write the transformation as a single composition.
b) What is the “straight-line” distance from the car’s starting point to the car’s ending point?
c) Using your answer from part (b), find the car’s average speed throughout the trip in miles per hour.