If A (3,1), B (-1,3), C (-3,-2) are the
vertices of A ABC, find the equation of
median AD.
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Answer:
Here, A(5,4),B(−3,−2) and C(1,−8) and AD is median.
∴ D is the midpoint of BC
∴D=(
2
−3+1
,
2
−2(−8)
)
=(−1,−5)
and equation of A(5, 4) and D(−1,−5) is
x−5
y−4
=
5−(−1)
4−(−5)
=
6
9
=
2
3
2y−8=3x−15
∴3x−2y−7=0 is the equation of median AD.
Now, Slope of AC=
5−1
4−(−8)
=
4
12
=3
The required line is parallel to AC and passes through B(−3,−2).
So, equation of required line is
y−(−2)=3[x−(−3)]
y+2=3x+9
y=3x+7
Hence, 3x−y+7=0 is the required equation of line.
Step-by-step explanation:
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