# Lesson 5

Squares and Circles

### Problem 1

Match each quadratic expression with an equivalent expression in factored form.​​​​​​

### Problem 2

An equation of a circle is $$x^2 - 8x + 16 + y^2 + 10y + 25 = 81$$.

1. What is the radius of the circle?
2. What is the center of the circle?

### Problem 3

Write 3 perfect square trinomials. Then rewrite them as squared binomials.

### Problem 4

Write an equation of the circle that has a diameter with endpoints $$(12,3)$$ and $$(\text-18,3)$$.

### Solution

(From Unit 6, Lesson 4.)

### Problem 5

1. Graph the circle $$(x-2)^2+(y-1)^2=25$$.
2. For each point, determine if it is on the circle. If not, decide whether it is inside the circle or outside of the circle.
1. $$(4,0)$$
2. $$(\text-3,3)$$
3. $$(\text-2,\text-2)$$
3. How can you use distance calculations to decide if a point is inside, on, or outside a circle?

### Solution

(From Unit 6, Lesson 4.)

### Problem 6

The triangle whose vertices are $$(2,5), (3,1),$$ and $$(4,2)$$ is transformed by the rule $$(x,y) \rightarrow (x-2,y+4)$$. 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

(From Unit 6, Lesson 3.)

### Problem 7

Technology required. A triangular prism has height 6 units. The base of the prism is shown in the image. What is the volume of the prism? Round your answer to the nearest tenth.