utes ago, the notorious crime syndicate Acute Perps struck again at the world-famous Wright Bank. Street reporter Stuart Olsen is live on the scene in Geo City. Let's go to Stuart now to find out more about these breaking developments. Stuart, what can you tell us?" "Well, Carl, at approximately 8:30 this morning, a trio of masked men overwhelmed security forces here at the Wright Bank in Geo City and robbed the bank of all its cash. This is the third robbery in as many days orchestrated by Acute Perps. According to police sources, the gang robs three locations in three days and then goes unseen for weeks before they strike again. Because this is their third robbery, officials expect the robbers will go underground for the next few weeks. However, the police need the help of Geo City citizens in the meantime. On your screen is a map of the locations Acute Perps has hit in the past three days." A triangle is shown on the coordinate plane. One vertex of the triangle, located at 6, 3 is labeled Cubic Storage. Another vertex at 6, negative 3 is labeled Geometric Gems. The third vertex at negative 2, negative 3 is labeled Wright Bank.
"This gang traditionally hits the three locations during each crime spree using the same pattern. Police are asking citizens to predict one of the next three locations Acute Perps will attack. They will use the information to stake out these locations in the coming weeks and bring Acute Perps to justice. Back to you, Carl." "Thanks, Stuart. It looks like the city has some important work to do!"
Step 1: Pick a Transformation
You have been asked by the police to find one of the three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle.
Step 2: Detailed Directions
For this step, identify and label three points on the coordinate plane that are a transformation of the original triangle. Next, follow the detailed directions listed here that correspond with the transformation you chose. Remember, you are only choosing one transformation to complete to help locate the gang.
If you chose translation, use the coordinates of your transformation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to receive full credit.
If you chose reflection, use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles to receive full credit.
If you chose rotation, use the coordinates of your rotation to show that the two triangles are congruent by the SAS postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles to receive full credit.
You must submit the construction of the original triangle and your transformation. You may create this graph using graphing technology. You may also print and use graph paper.
Step 3: Questions
Provide an answer to the question that matches your transformation. Because only one transformation was completed, only one of the following questions should be answered and submitted with your work:
Translation: Describe the translation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed. Be sure to use complete sentences in your answer.
Rotation: How many degrees did you rotate your triangle? In which direction (clockwise, counterclockwise) did it move? Be sure to use complete sentences in your answer.
Reflection: What line of reflection did you choose for your transformation? How are you sure that each point was reflected across this line? Be sure to use complete sentences in your answer.
