The circumcentre of the triangle formed by the points (1,2,3), (3,-1,5), (4,0,-3) is
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(1,1,1)
- $\left( {\frac{7}{2},\,\frac{1}{2},1} \right)$
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(3,3,3)
- $\left( {\frac{7}{2},\,\frac{{ - 1}}{2},1} \right)$
Reveal answer
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Correct answer
Explanation
The circumcenter (x,y,z) is equidistant from (1,2,3), (3,-1,5), and (4,0,-3). Setting the squared distances equal and solving the system of linear equations yields the coordinates (3.5, -0.5, 1).
AI explanation
The circumcentre is equidistant from the three vertices (1,2,3), (3,-1,5) and (4,0,-3), so we equate the distance squared from a point (x,y,z) to each vertex. Equating distances to the first two points gives x - 3y - z = -7, and equating distances to the first and third points gives x - 2y + 6z = -16. Solving this system of equations yields x = 7/2, y = -1/2, and z = 1, giving (7/2, -1/2, 1).