Q. 325.0( 2 Votes )

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

B.

C.

D.

Answer :

Given equation is y = 3x + 4 …(i)

Since, this equation is in y = mx + b form.


So, slope (m1) of the given equation is 3


Let equation of any line passing through the point (2, 3) is


y – y1 = m(x – x1)


y – 3 = m(x – 2) …(ii)


Given that eq. (i) is perpendicular to eq. (ii)


And we know that, if two lines are perpendicular then,


m1m2 = -1


3 × m2 = -1




Putting the value of slope in eq. (ii), we get



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 eq. (i) and (iii), we get


x + 3(3x + 4) – 11 = 0 [from(i)]


x + 9x + 12 – 11 = 0


10x + 1 = 0



Putting the value of x in eq. (i), we get






So, the required coordinates are


Hence, the correct option is (b)

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