find the distance of point (1/2, -1/3) from a line 4x + y + 7 = 0
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1
Answer:
The given lines are
2x−y=0...(1)
4x+7y+5=0....(2)
A(1,2) is point on line (1).
Let B be the point of intersection of lines (1) and (2).
On solving equation (1) and (2), we obtainx=
18
−5
andy=
9
−5
∴coordinates of point B are{
18
−5
,
9
−5
}
By using distance formula, the distance between point A and B can be obtained asAB=
{1+
18
5
}
2
+{2+
9
5
}
2
units
=
{
18
23
}
2
+{
9
23
}
2
units
=
{
2⋅9
23
}
2
+{
9
23
}
2
units
=
{
9
23
}
2
{
2
1
}
2
+{
9
23
}
2
units
=
(
9
23
)
2
(
4
1
+1)
units
=
9
23
4
5
units
=
9
23
⋅
2
5
units
=
18
23
5
units
Thus, the required distance is=
18
23
5
units
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