Question

Find the equation of the perpendicular drawn from the origin to the line 4x - 3y + 5 =0 .
Also find the coordinates of the foot of the perpendicular.

Answer 1

Answer:

The equation of perpendicular is" 3x + 4y = 0 ".

Co-ordinates of foot of perpendicular = (-4/5 , 3/5).

Step-by-step explanation:

Solution:

                  (A)

Since given equation is

4x -3y +5 =0        ............(1)

rearranging the equation (1) we get

y = (4/3)x  + 5/3   .............(2)

By comparing the equation (2) with standard equation" y = mx + c " we get

m=4/3    and  c = 5/3.

To find the equation of perpendicular to equation (2)

we know

Slope of perpendicular equation = (-1) / m

Putting m = 4/3 we get

Slope of perpendicular equation = -3 / 4

So

The equation of perpendicular is given as

   y = (-3/4)x + 5/3    ............(3)

Multiplying by 12 on both sides we get

   12y = (-9)x + 20

Rearranging the equation we get

  9x + 12y = 20        .............(4)

The equation (4) is the equation of perpendicular but it does not pass through origin.

To pass the equation (4) through origin the value of intercept  is must be "0" therefore we neglect the intercept "20"  to pass the equation (4) through the origin.So

  9x +12y = 0     ........(5)

Rearranging the equation (5) and subtracting by 3 we get

 3x + 4y = 0       ........(6)

The equation (6) is the required equation of perpendicular

                              (B)

To find the co-ordinates of foot of perpendicular.

We solve the equation (1) and equation (6)

By using equation (6) we get

y = (-3x) / 4       .............(7)

putting " y = (-3x) / 4 " in equation (1) we get

4x - 3 (-3x/4) + 5 = 0

⇒    x = -4/5  

putting value " x = -4/5 " in equation (7) we get

y = -3(-4/5)/4 = 12/20

⇒  y = 3/5

So co-ordinates of foot of perpendicular = (x , y)=(-4/5 , 3/5)

Hence co-ordinates of foot of perpendicular = (-4/5 , 3/5)

Answer 2

Answer:

easy understanding

refer to the attachment.