Question

find the distance from the line 4x+3y=5 to the point (6,9)

Answer 1

distance equation?

Answer 2

m=-4/3

y-9=-4/3(x-6)
y-9=-4/3x+8
y=-4/3x +17

(0, 5/3) and (6,9)
d=s.rt (6-0)^2+(9-5/3)^2
=9.47511

Answer 3

perhaps try this.

Answer 4

The distance from a point P(x,o,yo) to a line ax+by+c = 0 is

\[d=\frac{ \left| ax _{o}+by _{o}+c \right| }{ \sqrt{a^2+b^2} }\]

Answer 5

\[d=\frac{ \left| 4(6)+3(9)-5 \right| }{ \sqrt{4^2+3^2} }\]

Answer 6

been a while since I've done this so please correct me if i'm wrong

Answer 7

i got 9.2... but the hint say first find the line through the point (6,9) parallel to the given line, and then find the distance between these lines

Answer 8

you made a slight error on the slope of the line perpendicular to the given line
its slope is - 1 / (-4/3) = 3/4

Answer 9

- oh the parallel line ! sorry

Answer 10

so was it right or wrong?

Answer 11

chrs00's method is correct and that comes to 9.2

Answer 12

yep

Answer 13

why did you use (0,5/3) on the original line?

Answer 14

i think he just used any point on that line. i think you need to use a point that is perpendicular to that line

Answer 15

distance=shortest distance

Answer 16

are u sure ..this question is structure different frm the previous set of questions that i did..they want .. to find distance frm the point (a,b) eg.(4,8) to the line y=sumthing eg 6x+8y=9 ... inwhich i used that formula provide by chrs00

but the question ask to find the distance frm the line given to the point given...

Answer 17

Chris00 formula gives you just that

Answer 18

you were given a point that did not lie on that line

Answer 19

another way to do it is to find the equation of the line perpendicular to the original line and passing through the point (6,9)
then solving the 2 equations simultaneously to find the point of intersection.
Then use the distance formula with this point and (6,9)
But that's a bit long-winded.

Answer 20

ok

Answer 21

can u sketch it?

Answer 22

you can sketch it on the desmos web site

Answer 23

but i wouldnt get desmos to use in my test

Answer 24

the 2 parallel lines will look something like

Answer 25

ok

Answer 26

the line joining the point (0, 5/3) and (6,9) is not perpendicular to the 2 parallel lines. That is why you didn't get the right answer