The point A(1,2),B ( 3,-4) C (5,1) are the vertices of∆ABC find the equation of line passing through the midpoint of sides AB
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Step-by-step explanation:
Answer
A=(x
1
,y
1
)=(1,2)B=(x
2
,y
2
)=(4,6)C=(x
3
,y
3
)=(3,5)
Midpoint of AB=(
2
x
1
+x
2
,
2
y
1
+y
2
)
=(
2
1+4
,
2
2+6
)
=(
2
5
,
2
8
)=(
2
5
,4)
Midpoint of AC=(
2
x
1
+x
3
,
2
y
1
+y
3
)
=(
2
1+3
,
2
2+5
)
=(
2
4
,
2
7
)=(2,
2
7
)
∴ Equation of line passing through two points (
2
5
,4) and (2,
2
7
) by two point form is
⇒(y−y
1
)=
x
2
−x
1
y
2
−y
1
(x−x
1
)
⇒y−4=
2−
2
5
2
7
−4
(x−
2
5
)
⇒y−4=
4−5
7−8
(
2
2x−5
)
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