find point(x,y) on the line y=x using points
(-8,10) and(8,-7)

Question

find point(x,y) on the line y=x using points 
(-8,10) and(8,-7)

amistre64 · Answer

?

sabrina1 · Answer

ohhh sorry i for got to ADD equidistant point lol

amistre64 · Answer

:)  you want the point that is equidistant from the givens and that sits on y=x then right?

sabrina1 · Answer

yes lol :)

amistre64 · Answer

in other words; the place tha thte line cross

amistre64 · Answer

what kind of a line can we create with  the 2 given points?

amistre64 · Answer

or am i thinking of this erroneously .....

amistre64 · Answer

we need a distance formula perhaps

sabrina1 · Answer

welll yess i know we need the distance formula however since were lookimg for a set of points what would we replace it by in the  equation

amistre64 · Answer

(-8,10)                (8,-7)
-(x  , y)                -( x, y)
-----------------------
-8-x,10-y           8-x,-7-y

these are our respective distances from any point on y=x

amistre64 · Answer

this always gets messy when I try to do it  :)

sabrina1 · Answer

LOL :P at least youre honest. i started doing it and threw out half my copybook

amistre64 · Answer

$$\sqrt{x^2+16x+64+y^2-20y+100}$$                    equals
$$\sqrt{x^2-16x+64+y^2+14y+49}$$
as long as I did the squareing right that looks to be getting closer

amistre64 · Answer

we can square each one to get rid of the radicals and try to clean it up some:

$$x^2+16x+y^2-20y+164=x^2-16x+y^2+14y+113$$
$$16x-20y+164=-16x+14y+113$$
$$32x-20y+164=14y+113$$
$$32x+164=34y+113$$
$$32x+51=34y$$

hmmm

sabrina1 · Answer

i kinda get it but for some reason im also a little confused lol

amistre64 · Answer

yeah, its trying to use a distance formula to equate the distance from one point to the y=x line; with the other point

amistre64 · Answer

i think where this line and y=x cross is the point of interest tho

amistre64 · Answer

lets try it out :)

$$32x+51=34y$$
and since y=x

$$32x+51=34x$$
$$51=2x$$
$$51/2=x$$
perchance?

amistre64 · Answer

http://www.wolframalpha.com/input/?i=%2851%2F2%29^2%2B16%2851%2F2%29%2B%2851%2F2%29^2-20%2851%2F2%29%2B164%3D%2851%2F2%29^2-16%2851%2F2%29%2B%2851%2F2%29^2%2B14%2851%2F2%29%2B113++ the wolf says im good

sabrina1 · Answer

thats it! thats the answer to it
i just wanted to know how to come up with that. such a simple problem turns out to be not so simple. i very much appreciate it:)

amistre64 · Answer

just tough out the distance formulas and equate them

$$\sqrt{(x-Px_1)^2+(y-Py_1)^2}=\sqrt{(x-Px_2)^2+(y-Py_2)^2}$$

sabrina1 · Answer

thanks youve been a great help. midterms are the worst! lol

amistre64 · Answer

youre welcome :)  good luck