Question

Найдите точку, равноудаленную от точек A (6,7), B (3,3), C (1,-5) и вычислите это расстояние.

Answer 1

$A(6; 7); B(3; 3)\\k:\(x-6)^2+(y-7)^2=(x-3)^2+(y-3)^2\x^2-12x+36+y^2-14y+49=x^2-6x+9+y^2-6y+9\-12x-14y+85=-6x-6y+18\-14y+6y=-6x+12x+18-85\-8y=6x-67 /:(-8)\\underline{y=-frac{3}{4}x+frac{67}{8}}$


$B(3; 3); C(1;-5)\\l:\(x-3)^2+(y-3)^2=(x-1)^2+(y+5)^2\x^2-6x+9+y^2-6y+9=x^2-2x+1+y^2+10y+25\-6x-6y+18=-2x+10y+26\-6y-10y=-2x+6x+26-18\-16y=4x+8 /:(-16)\\underline{y=-frac{1}{4}x-frac{1}{2}}$


$-left{begin{array}{ccc}y=-frac{3}{4}x+frac{67}{8}\y=-frac{1}{4}x-frac{1}{2}end{array}right\--------------\. 0=-frac{2}{4}x+frac{67}{8}+frac{4}{8}\\. frac{1}{2}x=frac{71}{8} /cdot2\\. x=frac{71}{4}\\y=-frac{1}{4}cdotfrac{71}{4}-frac{1}{2}=-frac{71}{16}-frac{8}{16}=-frac{79}{16}\\O:left(frac{71}{4};-frac{79}{16}right)$