# 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

1. Draw the image of triangle $$ABC$$ under the transformation $$(x,y) \rightarrow (x-4,y+1)$$. Label the result $$T$$.
2. 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.

1. $$(x,y) \rightarrow (x-2,y-3)$$
2. $$(x,y) \rightarrow (2x,3y)$$
3. $$(x,y) \rightarrow (3x,3y)$$
4. $$(x,y) \rightarrow (2-x,y)$$

### 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 $$A''B''C''$$?

A:

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

B:

Reflect triangle $$ABC$$ across the line $$y=\text-x$$.

C:

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

D:

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 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.

### 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?

A:

1 cubic foot

B:

3 cubic feet

C:

9 cubic feet

D:

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.)