The angle between the lines formed by joining the points (2,-3), (-5, 1) and (7,-1), (0, 3) is
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Answer:
Here,
m
1
= Slope of line joining (-1,2) and (3,-5)
m
1
=
3+1
−5−2
=
4
−7
m
2
= Slope of line joining (-2,3) and (5,0)
m
2
=
5+2
0−3
=
7
−3
Let θ be the acute angle between the given lines, then
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
∣
1+(
4
−7
)(
7
−3
)
4
−7
−(
7
−3
)
∣
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
∣
∣
4
7
28
−37
∣
∣
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
49
−37
∣
∣
∣
∣
∣
tanθ=
49
37
θ=tan
−1
(
49
37
)
θ=37.05
o
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