Geometry | Unit 6 | Lesson 2: Transformations as Functions | Practice Problems

Match each coordinate rule to a description of its resulting transformation.

• Translate by the directed line segment from (0,0) to (0,4).

• Translate by the directed line segment from (0,0) to (3,0).

• Dilate using the origin as the center and a scale factor of 2.

• Translate by the directed line segment from (0,0) to (0,-4).

• Translate by the directed line segment from (0,0) to (-3,4).

Draw the image of triangle ABC under the transformation (x,y) → (x-4,y+1). Label the result T.

Draw the image of triangle ABC under the transformation (x,y) → (-x,y). Label the result R.

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

Reflect triangle ABC over the line x=0. Call this new triangle A’B’C’. Then reflect triangle A’B’C’ over the line y=0. Call the resulting triangle A''B''C''. Which single transformation takes ABC to A''B''C''?

• Translate triangle ABC by the directed line segment from (1,1) to (-2,1).

• Reflect triangle ABC across the line y=-x.

• Rotate triangle ABC counterclockwise using the origin as the center by 180 degrees.

• Dilate triangle ABC using the origin as the center and a scale factor of 2.

Reflect triangle ABC over the line y=2. Translate the image by the directed line segment from (0,0) to (3,2). What are the coordinates of the vertices in the final image?

The density of water is 1 gram per cm3. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a cylindrical log with radius 0.4 meters, height 5 meters, and mass 1,950 kilograms sink or float? Explain your reasoning.

These 3 congruent square pyramids can be assembled into a cube with side length 3 feet. What is the volume of each pyramid?

• 1 cubic foot

• 3 cubic feet

• 9 cubic feet

• 27 cubic feet

Reflect square ABCD across line CD. What is the ratio of the length of segment AA' to the length of segment AD? Explain or show your reasoning.