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  • The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by A. 37/10,-1/10 B. -1/10,37/10 C. 10/37,-10 D. 2/3,-1/3

The coordinates of the foot of perpendiculars from the point (2, 3) on the line y = 3x + 4 is given by

A. \frac{37}{10},\frac{-1}{10}

B. \frac{-1}{10},\frac{37}{10}

C. \frac{10}{37},-10

D. \frac{2}{3},-\frac{1}{3}

Answers (1)

Given equations are y=3x+4….(i) 

 Comparing this equation with y=mx+b form , the slope of the equation is 3. 

  Let the equation of any line passing through the point (2,3) is y-y1=m(x-x1)  

  y-3=m(x-2)……(ii)

  Given that equation (i) is perpendicular to equation (ii)

 And we know that, if two lines are perpendicular then m1m2= -1

   3*m2=-1 

 m2=-1/3 which is the slope of the required line  

   Putting the value of slope in equation ii  we get y-3=-1/3(x-2) 

   3y-9=-x+2    

 x+3y-9-2=0   

 x+3y-11=0……(iii)

 Now we have to find the coordinates of foot of the perpendicular

  Solving equation (i) and (iii)  we get x+3(3x+4)-11=0 

   x+9x+12-11=0  

 10x+1=0 

 x=-1/10 

 Putting the value of x in equation i , we get y=3(-1/10)+4   

    y= -3/10+4  

 y=37/10

  So the required coordinates are (-1/10,37/10)

Hence, the correct option is (b)

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