# Lesson 4

Distances and Circles

### Problem 1

Match each equation to its description.

### Solution

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### Problem 2

Write an equation of a circle that is centered at $$(\text-3,2)$$ with a radius of 5.

A:

$$(x-3)^2+(y+2)^2=5$$

B:

$$(x+3)^2+(y-2)^2=5$$

C:

$$(x-3)^2+(y+2)^2=25$$

D:

$$(x+3)^2+(y-2)^2=25$$

### Solution

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### Problem 3

1. Plot the circles $$x^2+y^2=4$$ and $$x^2+y^2=1$$ on the same coordinate plane.
2. Find the image of any point on $$x^2+y^2=4$$ under the transformation $$(x,y) \rightarrow \left(\frac{1}{2}x,\frac{1}{2}y\right)$$.
3. What do you notice about $$x^2+y^2=4$$ and $$x^2+y^2=1$$?

### Solution

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### Problem 4

$$(x,y) \rightarrow (x-3,4-y)$$ is an example of a transformation called a glide reflection. Complete the table using the rule.

Does this glide reflection produce a triangle congruent to the original?

input output
$$(1,1)$$ $$(\text-2,3)$$
$$(6,1)$$
$$(3,5)$$

### Solution

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(From Unit 6, Lesson 3.)

### Problem 5

The triangle whose vertices are $$(1,1), (5,3),$$ and $$(4,5)$$ is transformed by the rule $$(x,y) \rightarrow (3x,3y)$$. Is the image similar or congruent to the original figure?

A:

The image is congruent to the original triangle.

B:

The image is similar but not congruent to the original triangle.

C:

The image is neither similar nor congruent to the original triangle.

### Solution

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(From Unit 6, Lesson 3.)

### Problem 6

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

### Solution

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(From Unit 6, Lesson 2.)

### Problem 7

A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. It has a radius of 18 inches and a height of 6 inches. The cone starts filling up with water. What fraction of the volume of the cone is filled when the water reaches a height of 2 inches?

A:

$$\frac{1}{729}$$

B:

$$\frac{1}{27}$$

C:

$$\frac19$$

D:

$$\frac13$$

### Solution

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(From Unit 5, Lesson 14.)