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

Question

The coordinates of the foot of perpendicular 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) ((2/2), -(1/3))

Tardigrade Admin · Accepted Answer

Let the coordinates of foot of perpendicular be

A (α, β)

from the point

P (2, 3)

(say) on line

y = 3 x + 4

Slope of

A P

,

m_{1} = \frac{β - 3}{α - 2}

Slope of given line,

m_{2} = 3

Since, both are perpendicular.

∴ m_{1} \times m_{2} = - 1

\Rightarrow \frac{β - 3}{α - 2} \times 3 = - 1

\Rightarrow 3 β = - α + 11 \dots (i)

Also, the point

A (α, β)

is on the given line.
So,

A (α, β)

satisfy the equation of the line.

∴ β = 3 α + 4 \dots (ii)

On solving

(i)

and

(ii)

, we get

α = - \frac{1}{10}

,

β = \frac{37}{10}

So, coordinates of foot of perpendicular is

(\frac{- 1}{10}, \frac{37}{10})

.

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

$(\frac{37}{10}, \frac{- 1}{10})$

$(\frac{- 1}{10}, \frac{37}{10})$

$(\frac{10}{37}, - 10)$

$(\frac{2}{2}, - \frac{1}{3})$

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

(1037​,10−1​)

(10−1​,1037​)

(3710​,−10)

(22​,−31​)

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

$(\frac{37}{10}, \frac{- 1}{10})$

$(\frac{- 1}{10}, \frac{37}{10})$

$(\frac{10}{37}, - 10)$

$(\frac{2}{2}, - \frac{1}{3})$