Answer:
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Step-by-step explanation:
Let (a,b) be the coordinates of the foot of the perpendicular from the point (−1,3) to the line 3x−4y−16=0
Slope of the line joining (−1,3) and (a,b), is m
1
=
a+1
b−3
Slope of the line 3x−4y−16=0 or y=
4
3
x−4,m
2
=
4
3
Since these two lines are perpendicular,m
1
m
2
=−1
∴{
a+1
b−3
}⋅{
4
3
}=−1
⇒
4a+4
3b−9
=−1
⇒3b−9=4a−4
⇒4a+3b=5...(1)
Point(a,b) lies on line 3x−4y=16
∴3a−4b=16....(2)
On solving equation (1) and (2) we obtain
a=
25
68
and b=−
25
49
Thus, the required coordinates of the foot of the perpendicular are {
25
68
,
25
49
}
