Question

N(3,4)is the foot of the perpendicular drawn from the origin to line L.find the equation of line L​

Answer 1

Answer:3x-4y=25

Step-by-step explanation:

The perpendicular is drawn from origin to line L and we have to find equation of lineL

Let the perpendicular be ON

Here, O=(0,0) and N=(3,-4)

So slope of ON is

y2-y1/x2-x1=-4-0/3-0

Therefore, slope of ON is -4/3

Now ON is perpendicular to line L

Therefore we know that slope of line L(m)×slope of ON=-1

Therefore m×-4/3=-1

Therefore m=3/4

Now equation of line L using slope point form

y-y1=m(x-x1)

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

4y+16=3x-9

3x-4y=25

Therefore equation of line L is 3x-4y-25=0

Answer 2

Answer:

Step-by-step explanation:

Answer:3x-4y=25

Step-by-step explanation:

The perpendicular is drawn from origin to line L and we have to find equation of lineL

Let the perpendicular be ON

Here, O=(0,0) and N=(3,-4)

So slope of ON is

y2-y1/x2-x1=-4-0/3-0

Therefore, slope of ON is -4/3

Now ON is perpendicular to line L

Therefore we know that slope of line L(m)×slope of ON=-1

Therefore m×-4/3=-1

Therefore m=3/4

Now equation of line L using slope point form

y-y1=m(x-x1)

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

4y+16=3x-9

3x-4y=25

Therefore equation of line L is 3x-4y-25=0