Navigation

9-12 Integrated Math 2 Unit 2 Lesson 12

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

Unit

Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 •Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 2, Lesson 12

Weighted Averages

$Course Icon$

Integrated Math 2

Practice

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?

\((3,1.5)\)
\((4,2)\)
\((2,4)\)
\((3.5,3)\)

to access Practice Problem Solutions.

Problem 2

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

\((3,5)\)
\((4,3)\)
\((5,3)\)
\((5,5)\)

to access Practice Problem Solutions.

Problem 3

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

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

to access Practice Problem Solutions.

Problem 4

from an earlier course

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 \(ABCD\).

quadrilateral
parallelogram
rectangle
square

to access Practice Problem Solutions.

Problem 5

ForLesson 7: Evidence, Angles, and Proof

Lines \(AD\) and \(EC\) meet at point \(B\).

Give an example of a rotation using an angle greater than 0 degrees and less than 360 degrees that takes both lines to themselves. Explain why your rotation works.

<p>Lines AD and EC intersect at point B.</p>

to access Practice Problem Solutions.

Problem 6

ForLesson 7: Evidence, Angles, and Proof

Lines \(AB\) and \(BC\) are perpendicular. The dashed rays bisect angles \(ABD\) and \(CBD\).

Select all statements that must be true:

<p>Lines AB and BC are perpendicular and meet at point B. Dashed rays BF and BE bisect angles ABD and CBD.</p>

Angle \(CBF\) is congruent to angle \(DBF\).
Angle \(CBE\) is obtuse.
Angle \(ABC\) is congruent to angle \(EBF\).
Angle \(DBC\) is congruent to angle \(EBF\).
Angle \(EBF\) is 45 degrees.

to access Practice Problem Solutions.

Lesson 12 Resources

Student Materials