Triangle PST is a 45-45-90 degree triangle with vertices S(4, -3), T(-2,3) and m

Question

Triangle PST is a 45-45-90 degree triangle with vertices S(4, -3), T(-2,3) and m<S=90 degrees. P is in quadrant 1. Find the coordinates of P and give answer in simplest radical form...

I got the distance from T to P to be 12 units, but after that, i'm not sure what to do.

rizags · Answer

how did you get that distance?

rizags · Answer

i got it nevermind lol ok im working on it

rizags · Answer

my distance formula system of equations is not yielding a pretty answer lemme try something else

rizags · Answer

did you use the distance formula to find TP?

rizags · Answer

I GOT IT!

rizags · Answer

and its NOOOOT a raidcal

rizags · Answer

are you still hereEEE?

rizags · Answer

HELOOOOOOO>!???!?? i SOLVed It

anonymous · Answer

Oh sorry! I got disconnected! D:

rizags · Answer

ok are you here now?

rizags · Answer

tell me if you know what the distance formula is

anonymous · Answer

Okay the distance formula is $$d=\sqrt{(x _{1}-x _{2})+(y _{1}-y _{2)}}$$

rizags · Answer

so, we know the points S(4, -3), T(-2,3), and we know that
$$SP=6\sqrt{2}$$
and
$$TP=12$$

rizags · Answer

therefore, we can let the point at P be (x,y)

rizags · Answer

using the distance formula, one can create a system of two equations

rizags · Answer

that look like so:
$$6\sqrt{2}=\sqrt{(x-4)^{2}+(y-(-3))^{2}} and  12=\sqrt{(x-(-2))^{2}+(y-3))^{2}} $$

anonymous · Answer

And then we just solve the system for x and y?

rizags · Answer

the way I solved it was by looking at the second equation and thinking that all that stuff inside the radical has to be equal to 144, in order for the entire radical to be equal to 12. Furthermore, the only way this can occur is if x=10, and y=3. As it turns out this also works for the first equation!! the answer must be (10,3). Here is the wolfram alpha proof of solution, but actually full out solving these systems by hand would be incredibly tedious http://www.wolframalpha.com/input/?i=solve+12%3Dsqrt%28%28x%2B2%29%5E2%2B%28y-3%29%5E2%29%2C+6sqrt%282%29%3Dsqrt%28%28x-4%29%5E2%2B%28y%2B3%29%5E2%29%2C+for+x+and+y

rizags · Answer

by the way, that first solution given by wolfram alpha is invalidated by the question's given that THE point P is in QUADRANT 1, which means that the x and y values of the coordinate MUST both  be positive!!!

rizags · Answer

so yea, i think thats the answeR!!

anonymous · Answer

Thank you so so so much for this! I was having such a hard time with it. I checked the back of the book, and (10,3) is correct!

rizags · Answer

niiiiice!

rizags · Answer

kk fanned u lol