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# Plot points L and P

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Point K is located in (-3,2) ont the coordinate grid.

Plot a Point L so that it is 15 unit from point k and so that KL is not vertical or horizontal. Then, add Point P that is 1/3 the distance from K to L.

Jan 28, 2018

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Draw a circle with a radius of 15  and a center at (-3, 2)

The equation of this circle is

(x + 3)^2  + (y - 2)^2   = 225

Let point  L  be located at   ( m, 0)    where m is positive

So...we can determine m  by letting  y  = 0  in in the above equation...so we have...

(m + 3)^2  + (0 - 2)^2  =  225

(m + 3)^2  + (-2)^2  =  225

(m + 3)^2  + 4   =  225     subtract 4 from each side

(m + 3)^2  =  221            take the positive root of both sides

m  +  3   =  √ 221          subtract 3 from  both sides

m = √ 221  - 3

So  L =  ( √ 221  - 3 , 0 )

And we can find P thusly

[ -3 +  (1/3) ( √ 221  - 3 - - 3) ,  2  + (1/3)(0 - 2) ]  =

[ - 3 +  (1/3) (  √ 221 )  ,  2 + (1/3)(-2)  ]  =

[ -3 + √ 221/3   ,  2 - 2/3 ]  =

[ -3 + √ 221/3  , 4/3 ]

See the graph here : https://www.desmos.com/calculator/ggoirs81vs

Jan 29, 2018
edited by CPhill  Jan 29, 2018