find the equation of median AD in triangle ABC whose verices are A(1,3) B(0,4) and C(5,2)
Answers
Step-by-step explanation:
since AD,BE,CF are the medians of ΔABC
therefore D,E,F are the midpoints of BC,CA,AB respectively
Hence coordinates ofD=(
2
2+0
,
2
1+4
)=(1,
2
5
)
coordinate of E=(
2
0+(−1)
,
2
4+2
)=(
2
−1
,3)
coordinate of F=(
2
−1+2
,
2
2+1
)=(
2
1
,
2
3
)
Equation of median AD is given as ;
2−
2
5
y−
2
5
=
−1−1
x−1
⇒x−4y+9=0⟶(1)
Equation of median BE is given as;
1−3
y−3
=
2−(
2
−1
)
x−(
2
−1
)
⇒4x+5y−13=0⟶(2)
Equation of median CF is given as;
4−
2
3
y−
2
3
=
0−
2
1
x−
2
1
⇒10x+2y−8=0⟶(3)
Also the coordinate of the centroid O of ΔABC is given as ;
O
x
=
3
A
x
+B
x
+C
x
=
3
−1+2+0
=
3
1
O
y
=
3
A
y
+B
y
+C
y
=
3
2+1+4
=
3
7
∴(O
x
,O
y
)=(
3
1
,
3
7
)