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# find the point P(x,y)

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Line y =-x +6 has a point P(x,y) such that P is equidistant from  A(10,-10) and Origin. PA = PO. Find P.

I found that PA = sqrt((10-x)^2 + (10-y)^2) = sqrt (200 +x ^2+y^2 +2y-2x) and PO = sqrt(x^2 + y^2)

Since PA = PO and squaring both sides I get

x^2 +y^2-2x+2y+200 = x^2 + y^2

x-y = 10

So using graph I think P in the ordered form is (8,-2) (where PA=PO = sqrt(68))

Is this how I find P... am I missing anything?

Jan 29, 2021

### 4+0 Answers

#1
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I see no errors in your work, and your reasoning seems sound at first glance. I think you, geoNewbie21, have solved this problem correctly.

Jan 29, 2021
#2
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Good job geoNewbie  !!!

See the graph here : https://www.desmos.com/calculator/6wrak7ngnw

Notice that a cricle centered at (8, -2)    with a radius of  sqrt (68)   will go through  both the  origin and  (10-10)

So  PA  = PO   =  sqrt (68)   Jan 29, 2021
#3
+1

Thankyou Guest and CPhill,

CPhill could you actually share a link on how to use desmos.You have made it easy to understand/solve many geometry related questions, but I am not sure on how to use desmos to add the  points A and O in this case or plot the circle :)

Jan 29, 2021
#4
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I don't really have  a tuttorial on desmos

You  can download it from  their  site.....you can log in by supplying an email and password  so you  can share your graphs   (I believe these are "saved" so  it makes  logging in each time easy )

Just  type whatever equation , points, etc.,   you want  in the   boxes on the  left

If you  check  the label box  under each entry  it  will  display point coordinates.....you can also  customize this by typing  some identifier  on the  line  by the  label box   (for ex :   A = (1,0)  ).....you can add anything  on this  label line

I like desmos  OK,  but I tend to use Geogebra  more.....it is  a little harder to  use, but  it is ideal  for  drawing segments, etc......you  might explore  it, as well   CPhill  Jan 29, 2021