Question

perpendicular distance from point B(0,5) to the line x+3y-5=0

Answer 1

@virtus Are you here?

Answer 2

yes!

Answer 3

@virtus There maybe a direct formula for this, but I don't remember that. I'll start from the basics. Do you have time for this?

Answer 4

sure, thanks ash2326

Answer 5

Can I give the formula??

Answer 6

Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?

Answer 7

Go ahead @ash2326 ..

Answer 8

Let AB be our line and C is the point for which we need to find the perpendicular distance.
Do you understand the diagram?

Answer 9

yes

Answer 10

You can see that the perpendicular line from the point C is intersecting the line AB at a point. Let it be D
If we could find the coordinates of D, then we can easily find the distance.
do you have any ideas what should we do?

Answer 11

POI

Answer 12

POI???

Answer 13

find the Point Of Intersection

Answer 14

Ha ha ha ha..

Answer 15

Yeah:) @virtus
For that we need to find the equation of the line CD, do you have any idea how to do that?

Answer 16

well you know what point C is and the gradient of line CD would be -1/ gradient of line AB

Answer 17

oh wait do we know what C is ?

Answer 18

Awesome:D Could you do that?
We have AB
as
\(x+3y-5=0\)
Yeah we know C as (0, 5)

Answer 19

x+3y-15=0

Answer 20

Oops, You made a mistake
I can see that perpendicular line's slope is same as AB, it's to be -1/ slope AB
Check again :)

Answer 21

oh silly me

Answer 22

No problem, :D
find it again?

Answer 23

y-5 =3(x-0)
y=3x +5
3x-y+5=0