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Answers
Equation of line joining (6,−2) and (−8,7)
y−(−2)=
−8−6
7−(−2)
(x−6)
y+2=−
14
9
(x−6)
14y+28=−9x+54
14y+9x=26.....(i)
Slope of line =m
1
=−
b
a
=−
14
9
2y−3x+7=0
Slope of line =m
2
=−
b
a
=−
2
−3
=
2
3
3x=2y+7
Substituting in (i)
14y+3(2y+7)=26
14y+6y+21=26
20y=5
⇒y=
4
1
3x=2(
4
1
)+7
3x=
2
15
⇒x=
2
5
So the point of intersection is (
2
5
,
4
1
)
Angle between two lines i.e. tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
tanθ=
∣
∣
∣
∣
∣
∣
∣
∣
∣
1+(−
14
9
)(
2
3
)
−
14
9
−
2
3
∣
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
28
28−27
28
−18−42
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
28
1
28
−60
∣
∣
∣
∣
∣
∣
∣
∣
tanθ=60
⇒θ=tan
−1
60
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