# Lesson 2

Transformations as Functions

### Problem 1

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

### Solution

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### 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 \(R\).

### Solution

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### Problem 3

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

- \((x,y) \rightarrow (x-2,y-3)\)
- \((x,y) \rightarrow (2x,3y)\)
- \((x,y) \rightarrow (3x,3y)\)
- \((x,y) \rightarrow (2-x,y)\)

### Solution

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### 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.

### Solution

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(From Unit 6, Lesson 1.)### 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?

### Solution

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(From Unit 6, Lesson 1.)### Problem 6

The density of water is 1 gram per cm^{3}. 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.

### Solution

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(From Unit 5, Lesson 17.)### 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

### Solution

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(From Unit 5, Lesson 12.)### 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.

### Solution

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(From Unit 2, Lesson 1.)