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
- 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.
- IfBG=5, findGEandBE
- IfCG=16, findGFandCF
- IfAD=30, findAGandGD
- IfGF=x, findGCandCF
- IfAG= 9 xandGD= 5 x−1, findxandAD.
Use 4 ABCwithA(− 2 , 9 ),B( 6 , 1 )andC(− 4 ,− 7 )for questions 10-15.
- Find the midpoint ofABand label itM.
- Write the equation of
←→
CM.
- Find the midpoint ofBCand label itN.
- Write the equation of
←→
AN.
- Find the intersection of
←→
CMand
←→
AN.
- What is this point called?