Question

find the coordinates of the point equidistant from three given points  A(5,3) B(5,-5) C(1,-5).

Answer 1

Let the point be (x,y)
$(x-5)^2+(y-3)^2=(x-5)^2+(y+5)^2 \\ y^2-6y+9=y^2+10y+25 \\ 16y=-16 \\ y=-1$
$(x-1)^2+(y+5)^2=(x-5)^2+(y+5)^2 \\ x^{2} -2x+1= x^{2} -10x+25 \\ 8x=24 \\ x=3$
$(3,-1)$

Answer 2

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