# Lesson 3

Types of Transformations

### Problem 1

Complete the table and determine the rule for this transformation.

input output
$$(2,\text-3)$$ $$(\text-3,2)$$
$$(4,5)$$ $$(5,4)$$
$$(\rule{.5cm}{0.4pt},4)$$ $$(4,0)$$
$$(1,6)$$
$$(\text-1,\text-2)$$
$$(x,y)$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

Write a rule that describes this transformation.

original figure image
$$(5,1)$$ $$(2,\text-1)$$
$$(\text-3,4)$$ $$(\text-6,\text-4)$$
$$(1,\text-2)$$ $$(\text-2,2)$$
$$(\text-1,\text-4)$$ $$(\text-4,4)$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

Select all the transformations that produce congruent images.

A:

dilation

B:

horizontal stretch

C:

reflection

D:

rotation

E:

translation

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

Here are some transformation rules. For each transformation, first predict what the image of triangle $$ABC$$ will look like. Then compute the coordinates of the image and draw it.

1. $$(x,y) \rightarrow (x-4,y-1)$$
2. $$(x,y) \rightarrow (y,x)$$
3. $$(x,y) \rightarrow (1.5x,1.5y)$$

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 2.)

### Problem 5

A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height.

1. Find the volume of the cylinder.
2. Find the volume of the cone.
3. What fraction of the cylinder’s volume is the cone’s volume?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 13.)

### Problem 6

Reflect triangle $$ABC$$ over the line $$x=\text-2$$. Call this new triangle $$A’B’C’$$. Then reflect triangle $$A’B’C’$$ over the line $$x=0$$. Call the resulting triangle $$A''B''C''$$.

Describe a single transformation that takes $$ABC$$ to $$A''B''C''$$.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 1.)

### Problem 7

In the construction, $$A$$ is the center of one circle, and $$B$$ is the center of the other.

Explain why segments $$AC$$, $$BC$$, $$AD$$, $$BD$$, and $$AB$$ have the same length.