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Unit 4: Transformations, Congruency, and Similarity

Transformations

For all of the following questions. Show all work algebraically step by step. NO WORK, NO CREDIT. For problems 3-8 graph all the transformations as you go.

  1. The point A (3,4) is reflected across the x axis, then translated 3 units left. What is the new coordinate?
  1. Point H at coordinate (-1,4) is rotated 270° counterclockwise. Then translated (-10, 5) and finally reflected over the y axis. What is the new coordinate of Point H?
  1. Jerry plots the point J(-1,-2) on a coordinate grid for a scavenger hunt. He tells the participants how to get to the next coordinate by reflecting the point over the x axis and then translating it up 2 units (0, 2). What coordinate should the participants go to next? Draw a diagram.
  1. The restaurant, Hef-r-la proposed a building location at the coordinates of H(-2,0), F(-4,0), R(-2, -1), and L(-4,-1). The company decides to move the location and the builder must re-position the building by rotating it 270 degrees clockwise (Hint: Think about what position that is in counterclockwise) What would the new coordinates of the building be? Draw a diagram and show the mathematical proof.
  1. Miriam is trying to find directions to her friend’s house. Her friend is a really annoying math nerd who gives her the direction as follows: If your house is at A(-4,0), B(-4,2), C(-2,2) and D(-2,0) then all you need to do is reflect you house over Booth Road (y-axis) and translate your house (1, -5). Once you have done those to two things rotate your house 90o clockwise (Hint: Think about what position what is in counterclockwise.). Draw a diagram and show the mathematical proof.

6.  If triangle ABC were rotated 90° counterclockwise about the origin, then reflected over the x-axis, and finally translated (-8, -6) what would be the coordinates of B’?

7.  The diagram shows triangle ABC. Translate triangle ABC (-8, 5), then rotate it 270o counhterclockwise then flip it over the y-axis. Triangle ABC’s final coordinates?

8.  If hexagon ABCDEF were translated 2 units up and 4 units right, then flipped over the y-axis , and rotated 180o counterclockwise what would be the coordinates of point C’?