Navigation

9-12 Integrated Math 2 Unit 2 Lesson 13

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 13

Weighted Averages in a Triangle

$Course Icon$

Integrated Math 2

Practice

Problem 1

Triangle \(ABC\) and its medians are shown.

<p>Triangle ABC graphed. A = -2 comma 0, B = 0 comma 4, C = 3 comma 2. median CD, D = -1 comma 2. median BF, F = 0 point 5 comma 1. median AE, E = 1 point 5 comma 3. </p>

Select all statements that are true.

The medians intersect at \(\left(\frac{1}{3}, 2\right)\).
The medians and altitudes are the same for this triangle.
An equation for median \(AE\) is \(y=\frac{6}{7}(x+2)\).
Point \(G\) is \(\frac{2}{3}\) of the way from \(A\) to \(E\).
Median \(BF\) is congruent to median \(CD\).

Problem 2

Triangle \(ABC\) has vertices at \((\text-2,0), (\text-1,6),\) and \((6,0)\). What is the point of intersection of the triangle’s medians?

Problem 3

Triangle \(EFG\) and its medians are shown.

<p>Triangle EFG and its medians EH, FI, and GJ drawn.</p>

Match each pair of segments with the ratios of their lengths.

\(GK:KJ\)
\(GH:HF\)
\(HK:KE\)

\(1:1\)
\(1:2\)
\(2:1\)

Problem 4

ForLesson 12: Weighted Averages

Given \(A(\text-3,2)\) and \(B(7,\text-10)\), find the point that partitions segment \(AB\) in a \(1:4\) ratio.

Problem 5

ForLesson 12: Weighted Averages

Graph the image of quadrilateral \(ABCD\) under a dilation using center \(A\) and scale factor \(\frac{1}{3}\).

<p>Quadrilateral ABCD. Point A at 0 comma 0. Point B at 10 comma 6. Point C at 12 comma 18. Point D at negative 6 comma 6.</p>