In the below triangle, C is the centroid and KG, LF, and JH are all medians. If FC-2, find CL and LF. G. CL= LF%3 If HC=7x and CJ=6x+16, find the value of x, HC, CJ, and JH X= HCD CJ=

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In the given triangle, \( C \) is the centroid, and \( KG \), \( LF \), and \( JH \) are all medians. If \( FC = 2 \), find \( CL \) and \( LF \).

Diagram:
- The diagram shows a triangle with point \( C \) marked as the centroid.
- From \( C \), lines extend to \( F \), \( G \), and \( H \); these lines represent the medians.
- Points \( K \), \( L \), and \( J \) are connected to form the triangle’s vertices.

\( CL = \) [Blank]

\( LF = \) [Blank]

If \( HC = 7x \) and \( CJ = 6x + 16 \), find the value of \( x \), \( HC \), \( CJ \), and \( JH \).

\( x = \) [Blank]

\( HC = \) [Blank]

\( CJ = \) [Blank]

\( JH = \) [Blank]
Transcribed Image Text:In the given triangle, \( C \) is the centroid, and \( KG \), \( LF \), and \( JH \) are all medians. If \( FC = 2 \), find \( CL \) and \( LF \). Diagram: - The diagram shows a triangle with point \( C \) marked as the centroid. - From \( C \), lines extend to \( F \), \( G \), and \( H \); these lines represent the medians. - Points \( K \), \( L \), and \( J \) are connected to form the triangle’s vertices. \( CL = \) [Blank] \( LF = \) [Blank] If \( HC = 7x \) and \( CJ = 6x + 16 \), find the value of \( x \), \( HC \), \( CJ \), and \( JH \). \( x = \) [Blank] \( HC = \) [Blank] \( CJ = \) [Blank] \( JH = \) [Blank]
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