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Question

Find the coordinates of the foot of perpendicular, draw form the point (2,3) to line y=3x4 ?

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Solution

Given equation of line is;
y=3x4(1)where,m=3
since the equation of line perpendicular to (1) is given as;y=mx+c(2)
where, m=1m=13
also eqn (2) passes through (2,3)
then, 3=13.2+cc=113
equation (2) becomes y=13x+1133y=x+11(3)
solving (1) and (3) we get,
x=2310;y=2910
coordinate of foot of the perpendicular is (2310,2910)

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