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 (m_{1}) of the given equation is 3

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

y – y_{1} = m(x – x_{1})

⇒ 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,

**m _{1}m_{2} = -1**

⇒ 3 × m_{2} = -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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