CK-12 Geometry Concepts

5.4. Medians http://www.ck12.org

m=

− 4 − 4

0 −(− 2 )

=

− 8

2

=− 4

y=− 4 x+b

− 4 =− 4 ( 0 )+b

− 4 =b

The equation of the median isy=− 4 x− 4

2.HFis half ofBH. Use this information to solve forx. Fory,HCis two-thirds ofDC. Set up an equation for both.

1

2

BH=HForBH= 2 HF HC=

2

3

DCor

3

2

HC=DC

3 x+ 6 = 2 ( 2 x− 1 )

3

2

( 2 y+ 8 ) = 5 y− 16

3 x+ 6 = 4 x− 2 3 y+ 12 = 5 y− 16

8 =x 28 = 2 y

3. This statement is true. By definition, a median intersects a side of a triangle at its midpoint. Midpoints divide
   segments into two equal parts.

Practice

For questions 1-4, find the equation of each median, from vertexAto the opposite side,BC.

1.A( 9 , 5 ),B( 2 , 5 ),C( 4 , 1 )

2.A(− 2 , 3 ),B(− 3 ,− 7 ),C( 5 ,− 5 )

3.A(− 1 , 5 ),B( 0 ,− 1 ),C( 6 , 3 )

4.A( 6 ,− 3 ),B(− 5 ,− 4 ),C(− 1 ,− 8 )

For questions 5-9,B,D, andFare the midpoints of each side andGis the centroid. Find the following lengths.

5. IfBG=5, findGEandBE


6. IfCG=16, findGFandCF


7. IfAD=30, findAGandGD


8. IfGF=x, findGCandCF


9. IfAG= 9 xandGD= 5 x−1, findxandAD.

Use 4 ABCwithA(− 2 , 9 ),B( 6 , 1 )andC(− 4 ,− 7 )for questions 10-15.

10. Find the midpoint ofABand label itM.


11. Write the equation of

←→

CM.

12. Find the midpoint ofBCand label itN.


13. Write the equation of

←→

AN.

14. Find the intersection of

←→

CMand

←→

AN.

15. What is this point called?