Im having a massive brain fart at the moment and Hicky and Rayne are on

[Kirby]

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (9,5).
Write the length L of the hypotenuse as a function of x.

I have no clue how to do this at all. Help.

[Rayne]

hicky is an english major

[Kirby]

I don't know he's a smart guy.

[Solly]

hicky is an english major

well obviously that's the brain fart, Rayne

[Kirby]

Im imagining the end formula is going to be some sort of distance formula, how I get there and eliminate the Ys is beyond me.

[Kirby]

I think I have to make some sort of imaginary line, have it connect with imaginary points, and find the distance of the imaginary points in a forumula for distance...

[Hicky]

i seem to remember this is pretty early trigonometry but on account of being an english major i have forcefully forgot how to maths

[ElijahWyatt]

L=the square root of ((l9xl +5)/x)^2)+(l9xl+5)^2
Am i right?
x being the slope

Edited! 2ce now so its clear what i ment, i knew what i ment in my head, but wrote it wrong.

[Rayne]

the triangle is formed by the x axis and y axis. since it's a right triangle, the y intercept and x intercept are equal and the slope of the hypotenuse is -1.

use the point slope form of the equation of a line:

(y-y1)=m(x-x1)

(y-5)=-1(x-9)

y=-x+14

[Kirby]

nope

[ElijahWyatt]

wait what?

just because its a right traingle doesn't mean the middle piece is sloped in any specific way. The x axis leg could extend far longer than the y axis leg, meaning the slope of the line connecting the two(hypotnuse) would be really small making the line really big.

[Rayne]

fuck im retarded

[Rayne]

HOLD UP

[Kirby]

Its not an equilateral right triangle.

[Rayne]

there is no way to solve this without more information

[ElijahWyatt]

i edited my formula had a brain fart and used the slope i derived the forumla with instead of x, now it should be right.

[God]

hm im not sure immediately. i thought about constructing a function for y based on its limits but i dont think that'll work.

[Rayne]

the length can be any number above 392

[Kirby]

Its not an equilateral right triangle.

I mean isosceles.

[Rayne]

wait a second no it cant abifucwgofnqpegvfqwwd

[Rayne]

i hate myself right now

[ElijahWyatt]

im 99% sure im right.
The legth of it is based on the slope(the only unknown factor( so x) and a point on the line. I simplified a bunch of formulas into one easy formula, i can't believe i'm not correct.
Really someone explain how my formula doesn't work for every single slope value ever(slopes have to be negative btw)

[Rayne]

the triangle is formed by the x axis and y axis. since it's a right triangle, the y intercept and x intercept are equal and the slope of the hypotenuse is -1.

use the point slope form of the equation of a line:

(y-y1)=m(x-x1)

(y-5)=-1(x-9)

y=-x+14

not only is this wrong but it didnt even answer the question. WHAT THE FUCKING F

[ElijahWyatt]

SHIT WHEN I SAY 9x +5 i mean the slope absolute valued + 5

[God]

L=the square root of ((9x +5)/x)^2)+(9x+5)^2
Am i right?
x being the slope

Edited!

it wants a function of the coordinate x