Question

Find the distance from the point of intersection of the lines 2x+3y=10 and 3x-y=4 to the line 5x-6y=1

Answer 1

First find the point

set both your equations equal and solve for (x,y)
(you could probably even get it by guessing)

Then use the distance formula from a point to a line

Answer 2

The point is 2,2 but I think I'm using the formula for the distance from a point to a line incorrectly...

Could you show me how you'd do it?

Answer 3

Okay, the point is (2,2) and the line is 5x-6y=1

So the formula you can use is just
\[\sqrt{ax+by+c} \div \sqrt{a ^{2}}+b ^{2}\]

Where the point is (x,y) and the line is ax+by+c=0

Answer 4

oops.. the ax by and c terms chould all be squared under the root

Answer 5

actually looking again.. they aren't squared. the first formula is right

Answer 6

(without the square root)

Answer 7

yeah That's the formula I have

Answer 8

so the equation is actually just

|ax +by+c| / sqrt(a^2 + b^2 )

Answer 9

But I'm supposed to use the absolute value, right?

Answer 10

yeah

Answer 11

and that's what I think was making me do the question wrong

Answer 12

so it should be 3 right?

Answer 13

not -3

Answer 14

Yeah, but the answer is 0.38

Answer 15

So does the absolute value apply to the denominator too?

Answer 16

Well both terms are squared so it won't matter for the bottom

Answer 17

So... The bottom should be ... \[\sqrt{61}\] right?

Answer 18

yeah

Answer 19

Hallelujah the right answer! Finally :)
Thanks for your help :)

Answer 20

awwyeah :)