# Lesson 15

Weighted Averages

### Problem 1

Consider the parallelogram with vertices at $$(0,0), (4,0), (2,3),$$ and $$(6,3)$$. Where do the diagonals of this parallelogram intersect?

A:

$$(3,1.5)$$

B:

$$(4,2)$$

C:

$$(2,4)$$

D:

$$(3.5,3)$$

### Problem 2

What is the midpoint of the line segment with endpoints $$(1,\text-2)$$ and $$(9,8)$$?

A:

$$(3,5)$$

B:

$$(4,3)$$

C:

$$(5,3)$$

D:

$$(5,5)$$

### Problem 3

Graph the image of triangle $$ABC$$ under a dilation with center $$A$$ and scale factor $$\frac{2}{3}$$.

### Problem 4

A quadrilateral has vertices $$A=(0,0), B=(2,4), C=(0,5),$$ and $$D=(\text-2,1)$$. Prove that $$ABCD$$ is a rectangle.

### Solution

(From Unit 6, Lesson 14.)

### Problem 5

A quadrilateral has vertices $$A=(0,0), B=(1,3), C= (0,4),$$ and $$D=(\text-1,1)$$. Select the most precise classification for quadrilateral $$ABCD$$.

A:

B:

parallelogram

C:

rectangle

D:

square

### Solution

(From Unit 6, Lesson 14.)

### Problem 6

Write an equation whose graph is a line perpendicular to the graph of $$x=\text-7$$ and which passes through the point $$(\text-7,1)$$.

### Solution

(From Unit 6, Lesson 12.)

### Problem 7

Graph the equations $$(x+1)^2+(y-1)^2=64$$ and $$y = 1$$. Where do they intersect?

### Solution

(From Unit 6, Lesson 13.)

### Problem 8

A parabola has a focus of $$(2, 5)$$ and a directrix of $$y=1$$. Decide whether each point on the list is on this parabola. Explain your reasoning.

1. $$(\text{-}1,5)$$
2. $$(2 ,3)$$
3. $$(6,6)$$