Lesson 2
Transformations as Functions
- Let’s compare transformations to functions.
Problem 1
Match each coordinate rule to a description of its resulting transformation.
Problem 2
- Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (x-4,y+1)\). Label the result \(T\).
- Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (\text- x,y)\). Label the result \(R\).
Problem 3
Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.
- \((x,y) \rightarrow (x-2,y-3)\)
- \((x,y) \rightarrow (2x,3y)\)
- \((x,y) \rightarrow (3x,3y)\)
- \((x,y) \rightarrow (2-x,y)\)
Problem 4
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 \((\text-2,1)\).
Reflect triangle \(ABC\) across the line \(y=\text-x\).
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.
Problem 5
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?
Problem 6
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.
Problem 7
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
Problem 8
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.