PLEASE HELP ASAP Find the Circumcenter: Given A (-4,2), B(4,5), and C (3,-1) Round answers to the nearest hundred

9514 1404 393

  (0.37, 2.52)

Step-by-step explanation:

The circumcenter is the point of intersection of the perpendicular bisectors of the sides. For the purpose of writing equations for those, we need to know the difference in coordinates of the sides, and the midpoint.

  (∆x, ∆y) = B-A = (4, 5) -(-4, 2) = (4+4, 5-2) = (8, 3)

  (mx, my) = (B+A)/2 = ((4, 5) +(-4, 2))/2 = (0, 7/2)

Then the general form equation of the perpendicular bisector can be written as ...

  ∆x(x -mx) +∆y(y -my) = 0

  8(x -0) +3(y -7/2) = 0

  8x +3y -21/2 = 0 . . . .  collect terms

  16x +6y -21 = 0 . . . . .  eliminate the fraction

Similarly, the equation for the perpendicular bisector of BC will be ...

  (∆x, ∆y) = C -B = (3, -1) -(4, 5) = (-1, -6)

  (mx, my) = (C +B)/2 = ((3, -1) +(4, 5))/2 = (7/2, 2)

  -1(x -7/2) -6(y -2) = 0

Multiplying by -2, we have ...

  2x +12y -31 = 0

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Solving these equations by the "cross multiplication method", we find ...

  x = (6(-31) -(12(-21))/(16(12)-2(6)) = 66/180 ≈ 0.366667

  y = (-21(2) -(-31)(16))/180 = 454/180 ≈ 2.52222

Rounded to hundredths, the circumcenter is (0.37, 2.52).

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b

step-by-step explanation: