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Question

Find the foot of perpendicular from the point (−3,−4) on the line 4(x+2)=3(y−4).

A
(315,85)
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B
(315,85)
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C
(275,135)
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D
(275,135)
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Solution

The correct option is A (315,85)
Equation of the line is 4(x+2)=3(y4)
4x+8=3y12
4x3y=20

Let the foot of the perpendicular from point P(3,4) on the line is Q(a,b)
Slope of given line is 43

Then slope of line PQ is 34 ( m1m2=1 for perpendicular lines )

b+4a+3=34

4b+16=3a9

3a+4b=25 ......... (1)

Point Q(a,b) also lies on the line 4x3y=20

So,
4a3b=20 .......... (2)

Solving (1) and (2) we get,

a=315, b=85

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