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

Mathematics

2 answers:

ra1l [238]4 years ago

8 0

The coordinate of the circumecenter of a triangle is A

kvv77 [185]4 years ago

6 0

The circumcenter is equal distance from all 3 verices.
Using distance formula, equate distance to A with distance to C:
$(x+3)^2 +(y+4)^2 = (x+3)^2 + y^2$
The x terms cancel, Expand and solve for y:
$y^2 +8y+16 = y^2$
$y = -2$
Now do same thing for point A and B:
$(x+3)^2 + (y+4)^2 = (x-1)^2 + (y+4)^2$
y terms cancel
$x^2 +6x+9 = x^2-2x+1$
$x = -1$

Circumcenter is the point (-1,-2)

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Write an equation of the circle with center (-7, 4) and radius 8.

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answer

(x+7)^2 + (y-4)^2 = 64

set up equation

the equation of a circle is (x - h)^2 + (y - k)^2 = r^2

where h is the center x coordinate and k is the center y coordinate

values

from the point (-7,4) we know that h = -7 and k = 4

since the radius is 8, r^2 = 8^2 = 64

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