Cakeislifelol
Cakeislifelol Cakeislifelol
  • 02-12-2016
  • Mathematics
contestada

What are the coordinates of the circumcenter of a triangle with vertices A(−3,−4), B(1,−4), and C(−3,0)?

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aclay1026
aclay1026 aclay1026
  • 02-12-2016
the coordinate of the circumecenter of a triangle is A
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wizard123
wizard123 wizard123
  • 02-12-2016
The circumcenter is equal distance from all 3 verices.
Using distance formula, equate distance to A with distance to C:
[tex](x+3)^2 +(y+4)^2 = (x+3)^2 + y^2[/tex]
The x terms cancel, Expand and solve for y:
[tex]y^2 +8y+16 = y^2[/tex]
[tex]y = -2[/tex]
Now do same thing for point A and B:
[tex](x+3)^2 + (y+4)^2 = (x-1)^2 + (y+4)^2[/tex]
y terms cancel
[tex]x^2 +6x+9 = x^2-2x+1[/tex]
[tex]x = -1[/tex]

Circumcenter is the point (-1,-2)

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