Question

Find the shortest distance between a line and a point

Answer 1

perprendicualar

Answer 2

Yes, the perpendicular line.

Answer 3

y=5

Answer 4

The line is ment to be straight, BTW

Answer 5

5

Answer 6

Thanks. What is the way to show that with working though?

Answer 7

pythagorean thm shows that all other lines not perpendicular must have greater length

Answer 8

Therefore, @swissgirl?

Answer 9

@swissgirl ?

Answer 10

hello

Answer 11

d=|ax+by+c|/sqrt{a^2+b2}

Answer 12

Is this it?
\[d=\frac{|ax+by+c|}{\sqrt{a^2+b2}}\]

Answer 13

Huh, @mathmath333

Answer 14

yes

Answer 15

I have NO idea what that is, Could you explain please?

Answer 16

Whoops, wrote the wrong question. Sorry :(
Find a line that is perpendicular to x=10 and (4,5)

Answer 17

Do you know, @mathmath333 ?

Answer 18

Yup. So what is that line? y=5?

Answer 19

yes

Answer 20

K, thanks. But how would you do the working for that though?

Answer 21

u can find the equation of line f,as slope m = 0 thus y=5

y-y1=m(x-x1)

Answer 22

So you would use the equation:
\[y-y_1=m(x-x_1)\]
To find the slope of the equation y=5?

Answer 23

yes this would work

Answer 24

So would you sub in the values, \((4,5)\) for that equation?

Answer 25

-.-

Answer 26

@swissgirl ?

Answer 27

yes of cos

Answer 28

I am still confused though. When I look on the video on KhanAcademy, the equation was in y=mx+c form. Now, it is in x=c form. I am not sure what to do from there?

Answer 29

y-y1=m(x-x1)

y-y1=mx-mx1

y=mx-mx1+y1

Answer 30

-mx1+y1=c

Answer 31

u know what m is?

Answer 32

The gradient?

Answer 33

how do u find it

Answer 34

m=(y2-y1)/(x2-x1)

Answer 35

\[m=\frac{y_2-y_1}{x_2-x_1}\]

Answer 36

put the points (10.5) and (4,5) in the equation

y=mx-mx1+y1

u will find y=5

Answer 37

how did you get 10.5?

Answer 38

thats obvious through vision

Answer 39

That's the issue. I need to do ALL of this algebraicly, without making a graph :(

Answer 40

never leave a question without graphing

Answer 41

I am not allowed to for this question. I asked

Answer 42

--____--
w.e

Answer 43

?

Answer 44

Still confused :(

Answer 45

shortest distance is perpendicular distance between from point to line

Answer 46

that is draw perpendicular (or u can say direct distance ) fromthe point on line