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:

\((3.5,3)\)

Solution

For access, consult one of our IM Certified Partners.

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:

\((5,5)\)

Solution

For access, consult one of our IM Certified Partners.

Problem 3

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

Triangle ABC graphed on coordinate grid. A at 4 comma 2, B at 16 comma 8, C at 13 comma 14. 

Solution

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.

(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:

quadrilateral

B:

parallelogram

C:

rectangle

D:

square

Solution

For access, consult one of our IM Certified Partners.

(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

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 12.)

Problem 7

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

Blank coordinate plane with grid, origin O. Horizontal and vertical scale negative 10 to 10 by 2’s.

Solution

For access, consult one of our IM Certified Partners.

(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. \((6,6)\)

Solution

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 7.)