Lesson 15

Weighted Averages

  • Let’s split segments using averages and ratios.

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 \(\frac{2}{3}\).

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

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.

(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

(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 \((\text-7,1)\).

(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.
(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. \((6,6)\)
(From Unit 6, Lesson 7.)